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Chapter 11Resource Masters

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission isgranted to reproduce the material contained herein on the condition that suchmaterial be reproduced only for classroom use; be provided to students, teachers,and families without charge; and be used solely in conjunction with GlencoeCalifornia Mathematics, Grade 6. Any other reproduction, for use or sale, isprohibited without prior written permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240

ISBN: 978-0-07-878306-7MHID: 0-07-878306-2 CAGR6 CRM11

Printed in the United States of America

4 5 6 7 8 9 10 MAL 14 13 12 11 10 09

Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters

booklets are available as consumable workbooks in both English and Spanish.

MHID ISBNStudy Guide and Intervention Workbook 0-07-878871-4 978-0-07-878871-0

Skills Practice Workbook 0-07-878873-0 978-0-07-878873-4

Practice Workbook 0-07-878875-7 978-0-07-878875-8

Word Problem Practice Workbook 0-07-878877-3 978-0-07-878877-2

Spanish VersionsStudy Guide and Intervention Workbook 0-07-878872-2 978-0-07-878872-7Skills Practice Workbook 0-07-878874-9 978-0-07-878874-1Practice Workbook 0-07-878876-5 978-0-07-878876-5Word Problem Practice Workbook 0-07-878878-1 978-0-07-878878-9

Answers for Workbooks The answers for Chapter 11 of these workbooks can be found in the

back of this Chapter Resource Masters booklet.

StudentWorks Plus™ This CD-ROM includes the entire Student Edition test along with the

English workbooks listed above.

TeacherWorks Plus™ All of the materials found in this booklet are included for viewing,

printing, and editing in this CD-ROM.

Spanish Assessment Masters MHID: 0-07-878879-X ISBN: 978-0-07-878879-6

These masters contain a Spanish version of Chapter 11 Test Form 2A and Form 2C.

iii

Teacher’s Guide to Using the Chapter 11 Resource Masters .........................................iv

Chapter Resources Chapter 11 Student-Built Glossary ....................1Chapter 11 Family Letter (English) ....................3Chapter 11 Family Activity (English) ..................4Chapter 11 Family Letter (Spanish) ...................5Chapter 11 Family Activity (Spanish).................6Chapter 11 Anticipation Guide (English)............7Chapter 11 Anticipation Guide (Spanish) ..........8

Lesson 11-1 Area of ParallelogramsLesson Reading Guide ......................................9Study Guide and Intervention ..........................10Skills Practice...................................................11Practice ............................................................12Word Problem Practice ....................................13Enrichment .......................................................14Spreadsheet Activity ........................................15

Lesson 11-2 Area of Triangles andTrapezoidsLesson Reading Guide ....................................16Study Guide and Intervention ..........................17Skills Practice...................................................18Practice ............................................................19Word Problem Practice ....................................20Enrichment .......................................................21

Lesson 11-3 Circles andCircumferenceLesson Reading Guide ....................................22Study Guide and Intervention ..........................23Skills Practice...................................................24Practice ............................................................25Word Problem Practice ....................................26Enrichment .......................................................27Spreadsheet Activity ........................................28TI-73 Activity ....................................................29

Lesson 11-4 Area of CirclesLesson Reading Guide ....................................30Study Guide and Intervention ..........................31Skills Practice...................................................32Practice ............................................................33Word Problem Practice ....................................34Enrichment .......................................................35

Lesson 11-5 Problem-SolvingInvestigation: Solve a Simpler ProblemStudy Guide and Intervention ..........................36Skills Practice...................................................37Practice ............................................................38Word Problem Practice ....................................39

Lesson 11-6 Area of Complex FiguresLesson Reading Guide ....................................40Study Guide and Intervention ..........................41

Skills Practice...................................................42Practice ............................................................43Word Problem Practice ....................................44Enrichment .......................................................45

Lesson 11-7 Three-DimensionalFiguresLesson Reading Guide ....................................46Study Guide and Intervention ..........................47Skills Practice...................................................48Practice ............................................................49Word Problem Practice ....................................50Enrichment .......................................................51

Lesson 11-8 Drawing Three-Dimensional FiguresLesson Reading Guide ....................................52Study Guide and Intervention ..........................53Skills Practice...................................................54Practice ............................................................55Word Problem Practice ....................................56Enrichment .......................................................57

Lesson 11-9 Volume of PrismsLesson Reading Guide ....................................58Study Guide and Intervention ..........................59Skills Practice...................................................60Practice ............................................................61Word Problem Practice ....................................62Enrichment .......................................................63TI-73 Activity ....................................................64

Lesson 11-10 Volume of CylindersLesson Reading Guide ....................................65Study Guide and Intervention ..........................66Skills Practice...................................................67Practice ............................................................68Word Problem Practice ....................................69Enrichment .......................................................70

AssessmentStudent Recording Sheet.................................71Rubric for Scoring Pre-AP................................72Chapter 11 Quizzes 1 and 2 ............................73Chapter 11 Quizzes 3 and 4 ............................74Chapter 11 Mid-Chapter Test ...........................75Chapter 11 Vocabulary Test .............................76Chapter 11 Test, Form 1 ..................................77Chapter 11 Test, Form 2A................................79Chapter 11 Test, Form 2B................................81Chapter 11 Test, Form 2C................................83Chapter 11 Test, Form 2D................................85Chapter 11 Test, Form 3 ..................................87Chapter 11 Extended-Response Test ..............89Chapter 11 Standardized Test Practice............90

Answers..................................................A1–A42

Contents

iv

Teacher’s Guide to Using the Chapter 11 Resource Masters

The Chapter 11 Resource Masters includes the core materials needed for Chapter 11. Thesematerials include worksheets, extensions, and assessment options. The answers for thesepages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing on theTeacherWorks Plus™ CD-ROM.

Chapter ResourcesStudent-Built Glossary (pages 1–2) Thesemasters are a student study tool thatpresents up to twenty of the key vocabularyterms from the chapter. Students are torecord definitions and/or examples for eachterm. You may suggest that studentshighlight or star the terms with which theyare not familiar. Give this to students beforebeginning Lesson 11-1. Encourage them toadd these pages to their mathematics studynotebooks. Remind them to complete theappropriate words as they study each lesson.

Family Letter and Family Activity(pages 3–6) The letter informs yourstudents’ families of the mathematics theywill be learning in this chapter. The familyactivity helps them to practice problems thatare similar to those on the state test. A fullsolution for each problem is included.Spanish versions of these pages are alsoincluded. Give these to students to takehome before beginning the chapter.

Anticipation Guide (pages 7–8) Thismaster, presented in both English andSpanish, is a survey used before beginningthe chapter to pinpoint what students mayor may not know about the concepts in thechapter. Students will revisit this surveyafter they complete the chapter to see iftheir perceptions have changed.

Lesson ResourcesLesson Reading Guide Get Ready for theLesson reiterates the questions from thebeginning of the Student Edition lesson.Read the Lesson asks students to interpretthe context of and relationships amongterms in the lesson. Finally, RememberWhat You Learned asks students tosummarize what they have learned usingvarious representation techniques. Use as astudy tool for note taking or as an informalreading assignment. It is also a helpful toolfor ELL (English Language Learners).

Study Guide and Intervention Thismaster provides vocabulary, key concepts,additional worked-out examples and CheckYour Progress exercises to use as areteaching activity. It can also be used inconjunction with the Student Edition as aninstructional tool for students who havebeen absent.

Skills Practice This master focuses moreon the computational nature of the lesson.Use as an additional practice option or ashomework for second-day teaching of thelesson.

Practice This master closely follows thetypes of problems found in the Exercisessection of the Student Edition and includesword problems. Use as an additionalpractice option or as homework for second-day teaching of the lesson.

v

Word Problem Practice This masterincludes additional practice in solving wordproblems that apply the concepts of thelesson. Use as an additional practice or ashomework for second-day teaching of thelesson.

Enrichment These activities may extendthe concepts of the lesson, offer an historicalor multicultural look at the concepts, orwiden students’ perspectives on themathematics they are learning. They arewritten for use with all levels of students.

Graphing Calculator, ScientificCalculator, or Spreadsheet ActivitiesThese activities present ways in whichtechnology can be used with the concepts insome lessons of this chapter. Use as analternative approach to some concepts or asan integral part of your lesson presentation.

Assessment OptionsThe assessment masters in the Chapter 11Resource Masters offer a wide range ofassessment tools for formative (monitoring)assessment and summative (final) assessment.

Student Recording Sheet This mastercorresponds with the standardized testpractice at the end of the chapter.

Pre-AP Rubric This master providesinformation for teachers and students onhow to assess performance on open-endedquestions.

Quizzes Four free-response quizzes offerassessment at appropriate intervals in thechapter.

Mid-Chapter Test This 1-page testprovides an option to assess the first half ofthe chapter. It parallels the timing of theMid-Chapter Quiz in the Student Editionand includes both multiple-choice and free-response questions.

Vocabulary Test This test is suitable forall students. It includes a list of vocabularywords and 10 questions to assess students’knowledge of those words. This can also beused in conjunction with one of the leveledchapter tests.

Leveled Chapter Tests• Form 1 contains multiple-choice questions

and is intended for use with below gradelevel students.

• Forms 2A and 2B contain multiple-choicequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D contain free-responsequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.

• Form 3 is a free-response test for use withabove grade level students.

All of the above mentioned tests include afree-response Bonus question.

Extended-Response Test Performanceassessment tasks are suitable for allstudents. Sample answers and a scoringrubric are included for evaluation.

Standardized Test Practice These threepages are cumulative in nature. It includesthree parts: multiple-choice questions withbubble-in answer format, griddablequestions with answer grids, and short-answer free-response questions.

Answers• The answers for the Anticipation Guide

and Lesson Resources are provided asreduced pages with answers appearing in red.

• Full-size answer keys are provided for theassessment masters.

Chapter 11 1 Glencoe California Mathematics, Grade 6

Vocabulary TermFound

Definition/Description/Exampleon Page

base

center

circle

circumference

complex figure

composite figure

cone

cylinder

diameter

edge

face

NAME ________________________________________ DATE ______________ PERIOD _____

Student-Built Glossary

Ch

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NAME ________________________________________ DATE ______________ PERIOD _____

Student-Built Glossary (continued)11

Vocabulary TermFound

Definition/Description/Exampleon Page

height

lateral face

� (pi)

prism

pyramid

radius

rectangular prism

semicircle

sphere

three-dimensional figure

trianglar prism

vertex (vertices)

volume

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Family LetterNAME ________________________________________ DATE ______________ PERIOD _____


Dear Parent or Guardian:

People who work in industries such as art, construction, and

science study two-and-three-dimensional figures. Knowing

how to calculate area, surface area, and volume helps us

make decisions about how much material we need to cover

and fill things.

In Chapter 11, Measurement: Two-and-Three-Dimensional

Figures, your child will learn how to find the area of

parallelograms, triangles, trapezoids, circles, and complex figures.

Your child will also learn to identify and draw three-dimensional

figures, to find the volume of rectangular prisms and cylinders, and

to solve problems by solving a simpler problem. In the study of

this chapter, your child will complete a variety of daily classroom

assignments and activities and possibly produce a chapter project.

By signing this letter and returning it with your child, you agree

to encourage your child by getting involved. Enclosed is an

activity you can do with your child that practices how the math

we will be learning in Chapter 11 might be tested. You may also

wish to log on to ca.gr6math.com for self-check quizzes and

other study help. If you have any questions or comments, feel

free to contact me at school.

Sincerely,

Signature of Parent or Guardian ______________________________________ Date ________

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Family ActivityStandards Practice

NAME ________________________________________ DATE ______________ PERIOD _____


11

Fold the page along the dashed line. Work each problem on another piece of paper.Then unfold the page to check your work.

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1. A circular table has a diameter of 6 feet.

Which of the following is also true aboutthis table?

A The radius of this table is 2.5 feet.B The circumference of this circle is

about 18.84 feet.C The area of this circle is about 18.84

square feet.D The are of this circle is about 109

square feet.

Fold here.

Solution

1. Hint: The radius of a circle is half of thediameter. The formula for circumference isC � �d or 2�r. The formula for the areaof a circle is A � �r 2, and � � 3.14.

The radius of the table is half of thediameter, or 3, so Choice A is false.

The circumference of the circle iscalculated below.

C � �d� 3.14 � 6 ft �18.84 ft

Option B is true.

The answer is B.

2. Mrs. Andrew's homeroom is collectingchange to donate to the local homelessshelter. The container they are using isa cylinder.

What is the volume of the container?

A 140 square centimetersB 879.2 square centimetersC 980 cubic centimetersD 3,077.2 cubic centimeters

Solution

2. The formula for the volume of acylinder is V � �r2h, where r representsthe radius and h represents the height.

The formula for the volume of thecontainer is V � �r2h.

V � 3.14 � (7cm)2 � 20 cm � 3,077.2 cm3

Notice that the units are cubed becausewe multiplied cm by cm2. Units toexpress volume are always cubic.

The answer is D.

6 ft 7 cm

20 cm

Carta a la familiaNOMBRE ______________________________________ FECHA ____________ PERÍODO ___

Capítulo 11 5 Glencoe California Mathematics, Grade 6

Estimado padre o apoderado:

Los que trabajan en la industria del arte, la construcción y la

ciencia, estudian figuras bidimensionales y tridimensionales.

Saber calcular el área, el área de superficie y el volumen nos

ayuda a tomar decisiones sobre cuánto material necesitamos

para cubrir y rellenar cosas.

En el Capítulo 11, Medición: Figuras bidimensionales y tridi-

mensionales, su hijo(a) aprenderá a calcular el área de paralelo-

gramos, triángulos, trapecios, círculos y figuras complejos. Su

hijo también aprenderá a identificar y dibujar figuras tridimension-

ales, a calcular el volumen de prismas y cilindros rectangulares y a

resolver problemas resolviendo otros más simples. En el estudio de

este capítulo, su hijo(a) completará una variedad de tareas y

actividades diarias y es posible que trabaje en un proyecto del

capítulo.

Al firmar esta carta y devolverla con su hijo(a), usted se com-

promete a ayudarlo(a) a participar en su aprendizaje. Junto con

esta carta, va incluida una actividad que puede realizar con

él(ella) y la cual practica lo que podrían encontrar en las prue-

bas de los conceptos matemáticos que aprenderán en el

Capítulo 11. Además, visiten ca.gr6math.com para ver

autocontroles y otras ayudas para el estudio. Si tiene cualquier

pregunta o comentario, por favor contácteme en la escuela.

Cordialmente,

Firma del padre o apoderado ________________________________________ Fecha ______

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Actividad en familiaPráctica de estándares

NAME ________________________________________ DATE ______________ PERIOD _____


1. Una mesa circular tiene un diámetro de6 pies.

¿Cuál de los siguientes también secumple con respecto a esta mesa?

A El radio de esta mesa mide 2.5 pies.B La circunferencia de este círculo es

alrededor de 18.84 pies.C El área de este círculo es de unos

18.84 pies cuadrados.D El área de este círculo es de unos

109 pies cuadrados.

Doblen aquí.

Solución

1. Ayuda: El radio de un círculo es la mitaddel diámetro. La fórmula para la circunfe-rencia es C � �d ó 2�r. La fórmula para elárea de un círculo es A � �r2 y � � 3.14.

El radio de la mesa es la mitad del diá-metro ó 3; entonces, la opción A es falsa.

La circunferencia del círculo se calculaa continuación.

C � �d� 3.14 � 6 pies �18.84 pies

La opción B es verdadera.

La respuesta es B.

2. El aula de la Sra. Andrew recogemonedas para donarlas a un refugiolocal de desamparados. Utilizan uncilindro como recipiente.

¿Cuál es el volumen del recipiente?

A 140 centímetros cuadradosB 879.2 centímetros cuadradosC 980 centímetros cúbicosD 3,077.2 centímetros cúbicos

Solución

2. La fórmula para el volumen de un cilin-dro es V � �r2h, donde r es el radio y hes la altura.

La fórmula para el volumen delrecipiente es V � �r2h.

V � 3.14 � (7cm)2 � 20 cm � 3,077.2 cm3

Noten que las unidades son cúbicas por-que multiplicamos cm por cm2. Paraexpresar el volumen siempre se usanunidades cúbicas.

La respuesta es D.

7 cm

20 cm

6 pies

11

Doblen la página a lo largo de las líneas punteadas. Resuelvan cada problema en otra hoja de papel. Luego, desdoblen la página y revisen las respuestas.

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NAME ________________________________________ DATE ______________ PERIOD _____

Anticipation GuideMeasurement: Two- and Three-Dimensional Figures


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Step 2

Step 1

STEP 1 Statement STEP 2A, D, or NS A or D

1. The area of a parallelogram is the product of the length of its base and the length of its side.

2. The area of a triangle can be found if the length of the base and the height is known.

3. The area of any figure is given in square units.4. The diameter of a circle is the distance from the center to

any point of the circle.5. The circumference of a circle equals the product of � and

r2, where r is the radius of the circle.6. A � �(10)2 is the area of a circle with a diameter of 10 units.7. The area of an irregular shape may be found by separating

the shape into geometric shapes with known area formulas,then finding the sum of the areas of each smaller shape.

8. A rectangular prism has 6 faces and 8 vertices.9. All the faces of a pyramid must be triangles.

10. The top view of a rectangular solid could be a rectangle or a square.

11. A rectangular prism with a volume of 90 cubic units could have dimensions of 3, 4, and 6 units.

12. Since the base of a cylinder is a circle, the formula for the area of a circle is part of the formula for the volume of a cylinder.

Before you begin Chapter 11

• Read each statement.

• Decide whether you Agree (A) or Disagree (D) with the statement.

• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).

After you complete Chapter 11

• Reread each statement and complete the last column by entering an A or a D.

• Did any of your opinions about the statements change from the first column?

• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.

11

NOMBRE ______________________________________ FECHA ____________ PERÍODO ___

Ejercicios preparatoriosMedición: Figuras bidimensionales y tridimensionales

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PASO 2

Antes de comenzar el Capítulo 11

• Lee cada enunciado.

• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.

• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,escribe NS (No estoy seguro(a).

Después de completar el Capítulo 11

• Vuelve a leer cada enunciado y completa la última columna con una A o una D.

• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?

• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con losenunciados que marcaste con una D.

PASO 1

PASO 1 PASO 2A, D o NS

EnunciadoA o D

1. El área de un paralelogramo es el producto de la longitud de su base por la longitud de su lado.

2. El área de un triángulo se puede calcular si se conocen la longitud de la base y la altura .

3. El área de cualquier figura se da en unidades cuadradas.4. El diámetro de un círculo es la distancia desde el centro a

cualquier punto del círculo.5. La circunferencia de un círculo es igual al producto de � y

r2, donde r es el radio del círculo.6. A � �(10)2 es el área de un círculo con diámetro de 10 unidades.7. Puede calcularse el área de una figura irregular al separar la

figura en figuras geométricas cuyas fórmulas de área se conocen y luego sumar las áreas de cada figura más pequeña.

8. Un prisma rectangular tiene 6 caras y 8 vértices.9. Todas las caras de una pirámide deben ser triángulos.

10. La vista superior de un sólido rectangular puede ser un rectángulo o un cuadrado.

11. Un prisma rectangular con volumen de 90 unidades cúbicas puede tener dimensiones de 3, 4 y 6 unidades.

12. Dado que la base de un cilindro es un círculo, la fórmula del área para un círculo es parte de la fórmula del volumen para un cilindro.


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Less

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Lesson Reading GuideArea of Parallelograms

Get Ready for the LessonComplete the Mini Lab at the top of page 572 in your textbook. Writeyour answers below.

1. What is the value of x and y for each parallelogram?

2. Count the grid squares to find the area of each parallelogram.

3. On grid paper, draw three different parallelograms in which x � 5 unitsand y � 4 units. Find the area of each.

4. MAKE A CONJECTURE about how to find the area of a parallelogram if youknow the values of x and y.

Read the Lesson5. Explain how to find the height of a parallelogram.

6. Suppose you are asked to find the area of the parallelogram below. Is thegiven solution correct? Explain.

A � bhA � 12 � 5A � 60The area of the parallelogram is 60 square centimeters.

Remember What You Learned7. Because rectangles, rhombuses, and squares are all parallelograms, the

formula for finding the area of a parallelogram is also used to find theareas of each of these figures. Think of a way to remember that the areaof a parallelogram is the product of its base and height. For example,draw several parallelograms, rectangles, rhombuses, and squares andlabel the base and height for each. Write the formula for the area beloweach model.

3 cm5 cm

12 cm

11-1NAME ________________________________________ DATE ______________ PERIOD _____

6AF3.1, 6AF3.2

Example 1

Example 2

Exercises

Find the area of a parallelogram if the base is 6 inches and the height is 3.7 inches.

Estimate A � 6 � 4 or 24 in2

A � bh Area of a parallelogram

A � 6 � 3.7 Replace b with 6 and h with 3.7.

A � 22.2 Multiply.

The area of the parallelogram is 22.2 square inches. This is close to the estimate.

Find the area of the parallelogram at the right.

Estimate A � 10 � 10 or 100 cm2

A � bh Area of a parallelogram

A � 12 � 8 Replace b with 12 and h with 8.

A � 96 Multiply.

The area of the parallelogram is 96 square centimeters. This is close to the estimate.

Find the area of each parallelogram. Round to the nearest tenth ifnecessary.

1. 2. 3. 17 in.

16 in.

4.6 mm

8 mm

5 ft

13.2 ft

12 cm

8 cm

3.7 in.

6 in.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionArea of Parallelograms


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11-1

The area A of a parallelogram equals the product of its base b and its height h.

A � bh

The base is any side of a parallelogram.

The height is the length ofthe segment perpendicularto the base with endpointson opposite sides.

b

h

6AF3.1, 6AF3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeArea of Parallelograms


Less

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1. base � 5 ft 2. base � 9 in.height � 12 ft height � 2 in.

3. base � 6 cm 4. base � 4�25� yd

height � 5.5 cm height � 2 yd

5. base � 15.3 mm 6. base � 19.6 mheight � 8 mm height � 14.5 m

7. 8.

9. 10.

11. 12.

13. 14.

7 yd

24 ft

4.3 mm

12 mm

20 in.

11 in.45

2.3 cm

2 cm

12 ft

9 ft15 mm

11 mm

7 in.

4 in.

2 cm

3 cm

6AF3.1, 6AF3.2


1. 2. 3.

4. 5. 6.

7. 8. 9.

GEOGRAPHY Estimate the area of each state.

10. 11.

12. ALGEBRA A parallelogram has an area of240 square meters. Find the height of theparallelogram if the base is 20 meters.

13. ALGEBRA What is the base of a parallelogramif the height is 5 feet and the area is 65 square feet?

5 ft

b ft

A � 65 ft2

20 m

h m A � 240 m2

55 mi

135 mi NewJersey

260 mi

215 mi Iowa

1.5 yd

24 in.

2 ft

15 in.

18 ft

3 yd

13 ft 14 ft

15 ft14

0.9 cm

0.7 cm 0.8 cm

11 in.

8 in.

7 in.12

5.2 yd

1 yd

12 m

12 m

4.5 mm

8.2 mm

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeArea of Parallelograms


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeArea of Parallelograms


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1. SAILS Joyce wants to construct a sailwith the dimensions shown. How muchmaterial will be used?

14 ft

25 ft

2. SIGNS Pedro wants to make the sign inthe shape shown and needs to knowhow much material will be needed.What is the area of the sign?

30 in.

35 in.

YardSale

3. SHADING Alma’s engineering firm mustdetermine the area of the largestnoontime shadow that a proposedbuilding design will create. What is thearea of the shadow?

40 ft

56 ft

4. POOLS Tamika has designed a pool inthe shape shown. What is the area ofthe bottom of the pool if the surface isperfectly flat?

30 m20 m

5. CITY PLANNING Two parallel streets arecut across by two other parallel streetsas shown in the figure, cutting off aparcel of land in the shape of aparallelogram. Find the area of theparcel of land.

250 ft

340 ft

Main Street

Dresden Way

Colu

mbu

s Av

e.

Jeffe

rson

Ave

.

6. TARPS Neka wants to cut a tarp in theshape shown. What is the minimumamount of canvas cloth that he willneed?

36 ft

40 ft

6AF3.1, 6AF3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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11-1

Two Area PuzzlesCut out the five puzzle pieces at the bottom of this page. Then usethem to solve these two puzzles.

1. Use all five puzzle pieces to make 2. Use the four largest pieces to makea square with an area of 9 square a square with an area of 8 squareinches. Record your solution below. inches. Record your solution below.

2 in.

1 in.

1 in.

2 in.

2 in.

1 in2

6AF3.1, 6AF3.2

Exercises

Example 2

Example 1

NAME ________________________________________ DATE ______________ PERIOD _____

Spreadsheet ActivityAreas of Parallelograms


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You can use a spreadsheet to determine the area of a parallelogram.

Use a spreadsheet to find the area of a parallelogram with base equal to 5 inches and height equal to 4 inches.

Step 1 Use cell A1 of the spreadsheet for the base of the parallelogram and cell B1 for the heightof the parallelogram.

Step 2 In cell C1, enter an equals sign followed by the formula for the area of a parallelogram.The formula should be �A1*B1. Then press ENTER to return the area.

The area of the parallelogram is 20 square inches.

Use a spreadsheet to find the area of a

parallelogram with base equal to 2.5 centimeters and height equal to 3.5 centimeters.

Step 3 Enter the base in cell A2 andthe height in cell B2.

Step 4 Click on the bottom right corner of cell C1 and drag it to C2. This returns the area of theparallelogram.

The area of the parallelogram is 8.75 square centimeters.

Use a spreadsheet to find the areas of the given parallelograms.

1. b � 3 in., h � 6 in. 2. b � 2 in., h � 5 in. 3. b � 5 in., h � 1 in.

4. b � 7 in., h � 3 in. 5. b � 3.5 m, h � 1.5 m 6. b � 2.2 m, h � 1.7 m

7. b � 1.5 m, h � 0.1 m 8. b � 5.7 m, h � 9.1 m 9. b � 0.5 m, h � 0.3 m

A B DC1234 Sheet 1

5 2.5 202.5 3.5 8.75

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideArea of Triangles and Trapezoids


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11-2


1. What is the area of the parallelogram?

2. Cut along the diagonal. What is true about the triangles formed?

3. What is the area of each triangle?

4. If the area of a parallelogram is bh, then write an expression for the areaA of each of the two congruent triangles that form the parallelogram.

Read the Lesson5. In a triangle, which side is the base?

6. How do you find the height of a triangle?

7. For what kind of triangle might the height be found outside of thetriangle?

8. How is the height of a trapezoid similar to the height of a triangle or parallelogram?

Remember What You Learned9. The Mini Lab in this lesson gave you a good way to remember the

formula for the area of a triangle by showing you that it is half the areaof a parallelogram, so A � �

12�bh. Think of a way to help you remember the

formula for the area of a trapezoid. Do you recognize anything in the

formula A � �12�h(b1 � b2)?

6AF3.1, 6AF3.2

Exercises

Example 2

Example 1

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionArea of Triangles and Trapezoids


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Find the area of the triangle.

Estimate �12

�(6)(5) � 15

A � �12�bh Area of a triangle

A � �12� � 6 � 4.5 Replace b with 6 and h with 4.5.

A � 13.5 Multiply.

The area of the triangle is 13.5 square inches. This is close to the estimate.

Find the area of the trapezoid.

A � �12�h(b1 � b2) Area of a trapezoid

A � �12�(4)(3 � 6) Replace h with 4, b1 with 3, and b2 with 6.

A � 18 Simplify.

The area of the trapezoid is 18 square centimeters.

Find the area of each figure. Round to the nearest tenth if necessary.

1. 2. 3. 4. 8 cm

13.5 cm

18 cm

7 in.

5 in.

14 in.

7 mm

9 mm12 ft

7 ft

4 cm

3 cm

6 cm

4.5 in.

6 in.

The area A of a triangle equals half the product of its base b and its height h.

A � �12�bh

A trapezoid has two bases, b1 and b2. The height of a trapezoid is the distance between the two bases. The area A of a trapezoid equals half the product of the height h and the sum of the bases b1 and b2.

A � �12�h(b1 � b2)

b1

b2

h

The base of atriangle can beany of its sides.

The height is thedistance from a baseto the opposite vertex.

b

h

6AF3.1, 6AF3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeArea of Triangles and Trapezoids


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11-2


1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. triangle: base � 16 cm, height � 9.4 cm

12. triangle: base � 13.5 in., height � 6.4 in.

13. trapezoid: bases 22.8 mm and 19.7 mm, height 36 mm

14. trapezoid: bases 5 ft and 3�12� ft, height 7 ft

14 mm

3.8 mm

15.3 mm

7.5 cm

12.2 cm

5.6 in.

6.9 in.12 ft

20.1 ft

25 ft

24 mm

20.7 mm7 cm

9.2 cm

2 cm

4 ft

3 ft

6.5 ft

12 mm

18 mm

10 mm

3 ft

2 ft10 cm

9 cm

6AF3.1, 6AF3.2


1. 2. 3.

4. 5. 6.

7. GEOGRAPHY The shape of Arkansas is roughly trapezoidal with bases of 150 miles and 250 miles and a height of 260 miles.What is the approximate area of Arkansas?

ALGEBRA Find the height of each figure.

8. Area � 23,000 m2 9. Area � 6,460 in2

Draw and label each figure. Then find the area.

10. a trapezoid with a height less than 11. a right triangle with a base greater5 feet and an area greater than than 10 meters and an area greater than50 square feet 75 square meters

136 in.

196 in. x in.

275 m

x m

125 m

150 mi

250 mi

260 mi Arkansas

10.1 mm

7 mm

9 yd

5 yd

4 yd

3 yd12

18.4 cm

12 cm

3.6 m

4 m

6.3 m

5 in.

5 in.34

7 ft

7 ft

11 ft

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeArea of Triangles and Trapezoids


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeArea of Triangles and Trapezoids


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11-2

1. GEOGRAPHY Arkansas has a shape thatis similar to a trapezoid with bases ofabout 182 miles and 267 miles and aheight of about 254 miles. Estimate thearea of the state.

2. PATIOS Greta is making a patio withthe dimensions given in the figure.What is the area of the patio?

15 ft

15 ft

8 ft

3. FLAGS Malila wants to make theInternational Marine Signal flag shownwhich represents the number six. Whatis the area of the flag?

30 in.100 in. 5 in.

4. SIGNS Estimate the area of the yieldsign.

30 in.

26 in.

5. TILING A ceramics company wants toproduce tiles in the shape shown. Whatis the area of the surface of each tile?

8.5 cm

8.5 cm

6. GARDENING Kinu wants to buy topsoilfor a section of her garden that has thedimensions shown in the figure. Whatis the area of this section of Kinu’sgarden?

4 yd

3.5 yd

4 yd

6AF3.1, 6AF3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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Heron’s FormulaA formula named after Heron of Alexandria, Egypt, can be used to findthe area of a triangle given the lengths of its sides.

Heron’s formula states that the area A of a triangle whose sides measurea, b, and c is given by

A � �s(s�a�)(s�b)�(s�c)�,

where s is the semiperimeter:

s � �a �

2b � c�.

Estimate the area of each triangle by finding the mean of the innerand outer measures. Then use Heron’s Formula to compute a moreexact area. Give each answer to the nearest tenth of a square unit.

1. 2. 3.

Estimated area: Estimated area: Estimated area:

Computed area: Computed area: Computed area:

4. 5. 6.

Estimated area: Estimated area: Estimated area:

Computed area: Computed area: Computed area:

9

57

8

83

7

77

6

8

109

9

106

66

6AF3.1, 6AF3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideCircles and Circumference


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11-3

Get Ready for the LessonRead the introduction at the top of page 584 in your textbook. Writeyour answers below.

1. Which point appears to be the center of the Ferris wheel?

2. Is the distance from G to F greater than, less than, or equal to thedistance from G to J?

3. What can you say about the distance from G to H and the distance from F to J?

4. Find the distance from G to F.

Read the Lesson5. The Greek letter � represents a nonterminating and nonrepeating

number. What does this mean?

6. When is the symbol � used when finding the circumference of a circle?Why is this symbol used?

7. What two numbers are used in this lesson as approximations for �?

Remember What You Learned8. The word diameter comes from two Greek words that mean “a measure

(metron) through (dia).” What is the diameter of a circle?

9. One of the definitions given for radius is semidiameter. Think of therelationship between radius and diameter. What do you thinksemidiameter means?

6MG1.1, 6MG1.2

Example 1

Example 2

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionCircles and Circumference


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Find the circumference of a circle with a diameter of7.5 centimeters.

C � �d Circumference of a circle.

C � 3.14 � 7.5 Replace � with 3.14 and d with 7.5.

C � 23.55 The circumference of the circle is about 23.55 centimeters.

If the radius of a circle is 14 inches, what is its circumference?

C � 2�r

C � 2 � 3.14 � 14 Replace � with 3.14 and r with 14.

C � 87.92 The circumference of the circle is about 87.92 inches.

Find the circumference of each circle. Use 3.14 for �. Round to thenearest tenth if necessary.

1. 2. 3. 4.

5. diameter � 15 km 6. radius � 21 mi 7. radius � 50 m

8. diameter � 600 ft 9. radius � 62 mm 10. diameter � 7 km

11. radius � 95 in. 12. diameter � 6.3 m 13. diameter � 5�14� cm

7.5 in. 5 m 20 cm 6 ft

A circle is the set of all points in a plane that are the same distance from a given point, called thecenter. The diameter d is the distance across thecircle through its center. The radius r is the distance from the center to any point on the circle. The circumference C is the distance around thecircle. The circumference C of a circle is equal to itsdiameter d times �, or 2 times its radius r times �.

circumference

radius

center

diameter

6MG1.1, 6MG1.2

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeCircles and Circumference


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11-3

Find the circumference of each circle. Use 3.14 for �. Round to the nearest tenth if necessary.

1. 2.

3. 4.

5. 6.

7. radius � 3 km 8. radius � 46 cm

9. diameter � 30 in. 10. diameter � 25 m

11. radius � 5 ft 12. diameter � 9�12� in.

13. radius � 3�12� ft 14. diameter � 9.7 mm

15. radius � 5.2 km 16. diameter � 12 m

17. radius � 22 ft 18. diameter � 9.4 in.

19. radius � 100 m 20. radius � 65 mi

21. diameter � 10�12� in. 22. diameter � 8.5 cm

4 in. 15 cm

8 ft21 m

16 km

37 mm

6MG1.1, 6MG1.2

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeCircles and Circumference


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Find the circumference of each circle. Use 3.14 for π. Round to thenearest tenth if necessary.

1. 2. 3.

4. 5. 6.

7. radius � 2�13

� ft 8. radius � 11.9 m 9. diameter�5�56

� mi

10. radius � 6�18

� in. 11. diameter � 17�12

�ft 12. radius � 9.2 km

Estimate to find the approximate circumference of each circle.Explain which approximation of π you used.

13. 14. 15.

ALGEBRA Find the diameter or radius of each circle. Use 3.14 for π.Round to the nearest tenth if necessary.

16. C � 32 m, diameter � ___ 17. C � 55 mi, radius � ___

18. HELICOPTERS The landing circle for helicopters on the roof of a hospitalhas a radius of 20 yards. To the nearest yard, find its circumference.

19. SPA A circular spa has a diameter of 12 feet. The spa is decorated with 4-inch porcelain tiles around the rim. How many tiles surround the rim ofthe spa? Round to the nearest whole tile.

59 in.4.1 cm

5 ft18

7 in.12 m4.2 mm

1.5 yd28 ft2.4 cm

6MG1.1, 6MG1.2

NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeCircles and Circumference


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11-3

1. PLATES A manufacturing company isproducing dinner plates with adiameter of 12 inches. They plan to puta gold edge on each plate. Determinehow much gold edging they need foreach plate by finding the circumferenceof each plate. Round to the nearesttenth.

2. MONEY A dime has a radius of 8�12�

millimeters. Find the circumference ofa dime to the nearest tenth.

3. MERRY-GO-ROUND Mr. Osterhout isputting trim around the edge of acircular merry-go-round that has adiameter of 15 feet. How much trimdoes he need to buy to the nearesttenth?

4. PIZZA Find the circumference of a pizzawith a diameter of 10 inches. Round tothe nearest tenth.

5. RACING A circular racetrack has adiameter of �

12� mile. How far does a car

travel in one lap around the track?Round to the nearest tenth.

6. TIRE A bicycle tire has a radius of 15inches. What is the circumference ofthe tire? Round to the nearest tenth.

7. EQUATOR Earth’s diameter at theequator is 7,926 miles. Find thedistance around Earth at its equator tothe nearest tenth.

8. SATURN The ring system aroundSaturn has a diameter of 170,000miles. Find the circumference of thering system.

6MG1.1, 6MG1.2

Finding the Length of an Arc

Recall that the circumference is the measure of the distance around acircle. A portion of the circumference is called an arc. An arc isnamed by the endpoints of the radii that create it. To find themeasure of an arc, you can use a proportion. The ratio of the arclength to the circumference is equal to the ratio of the central angleof the arc to 360º.

To find the measure of AB�, first set up the ratio. �m2�

AB�

r� � �

m�

36A0C°

B�

Next, fill in the known values. �m

4A�B�

� � �34600°°

�

Simplify the fraction. �m

4A�B�

� � �19

�

Then solve for m AB�. m AB��

49�� 1.40 cm

Solve the following problems.

1. A circle has a circumference of 48 centimeters. Find the length of an arc

that has a central angle of 90º. �m

4A8B�

� � �39600°

�,

2. A circle has a circumference of 112 meters. The length of DF� is 14 meters.

Find the measure of the central angle of DF�. �11142

� � �36

x0°�,

3. A circle has a radius of 5 inches. Find the length of an arc that has a

central angle of 72º. �m10

A�B�

� � �37620°°

�,

4. Two arcs in a circle have central angles of 135º and 45º. Find the ratio of

the arcs’ lengths. �14355°°

�,

5. AB� has a central angle of 50º in a circle whose diameter is 12 feet, whileDEF� has a central angle of 150º in a circle whose diameter is 3 feet.

Which of these two arcs is longer? Explain.

40˚

2 cmC

A

B

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Spreadsheet ActivityExploring the Value of �


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11-3

You can use a spreadsheet to explore the value of �. You will need at least10 different circular items. These could be cups, lids, cans, or even thecircular markings on the gym floor or the outline of a basketball hoop.Carefully measure the circumference of each item with a piece of string.Then use a metric ruler to record the measurement in millimeters. Alsorecord the measure of the diameter of each object in millimeters.

Create a spreadsheet with three columns. In column A, enter thecircumferences of the items you measured. In column B, enter thediameters. In column C, create a formula for the value of � usingcircumference and diameter. Let the spreadsheet calculate the value for asmany decimal places as it can.

Your spreadsheet should look like this.

Use your spreadsheet to answer the following questions.

1. What is the value of � used by your spreadsheet?

2. How close are your calculations to the actual value of �? To how many decimal places are your calculations correct?

3. What causes your calculations of � not to be exact?

Sample 4. What could make your calculations more exact?

5. Suppose you created another spreadsheet with the same columns as this one. The new spreadsheet calculates the diameter when given the circumference and the value of �. What formula would you enter in column B?

6. If you create another spreadsheet that calculates the circumference when given the diameter and the value of �, what formula would you enter in column A?

A B DC123 Sheet 1

27 8 3.375

6MG1.1, 6MG1.2

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

TI-73 ActivityCalculating Circumference


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The [�] key makes it easier to evaluate expressions that use the constant pi, �.

Find the circumference of a circle with a radius of 8 meters. Express youranswer to the nearest tenth.

C � 2�r

2 [π] 8

The circumference is about 50.3 meters.

Find the circumference of each circle to the nearest tenth.

1. 2.

3. 4.

5. 6.

6.9 cm8.3 ft

7.4 m11 in.

18 ft6 m

ENTER2nd

2nd

Example

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideArea of Circles


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11-4


1. What is the measurement of the base and the height?

2. Substitute these values into the formula for the area of a parallelogram.

3. Replace C with the expression for the circumference of a circle, 2�r.Simplify the equation and describe what it represents.

Read the Lesson4. The formula for the area of a circle uses the number �. How does this

affect the value of the area of a circle found using the formula?

5. If you are given the length of the diameter of a circle, how can you find itsarea?

Remember What You Learned6. Think about the formulas you have learned that involve circles: C � 2�r

or C � �d and A � �r2. To help you remember the difference between theformulas for circumference and the formula for area, think about thedifferences in the units used for each measurement. What kinds of unitsare used for each? How can this help you remember the formula for thearea of a circle?

6MG1.1, 6MG1.2

Exercises

Example 2

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionArea of Circles


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Find the area of the circle.

A � �r2 Area of circle

A � 3.14 � 52 Replace � with 3.14 and r with 5.

A � 78.5

The area of the circle is approximately 78.5 square centimeters.

Find the area of a circle that has a diameter of 9.4 millimeters.

A � �r2 Area of a circle

A � 3.14 � 4.72 Replace � with 3.14 and r with 9.4 2 or 4.7.

A � 69.4

The area of the circle is approximately 69.4 square millimeters.

Find the area of each circle. Use 3.14 for �. Round to the nearest tenth.

1. 2. 3.

4. radius � 2.6 cm 5. radius � 14.3 in. 6. diameter � 5�12� yd

7. diameter � 4�34

� mi 8. diameter � 7.9 mm 9. radius � 2�15� ft

12 ft

25 mm7 in.

5 cm

The area A of a circle equals the product of pi (�) and the square of its radius r.

A � �r 2

Example 1

6MG1.1, 6MG1.2

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeArea of Circles


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11-4

Find the area of each circle. Use 3.14 for π.Round to the nearest tenth.

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. radius � 5.7 mm 12. radius � 8.2 ft

13. diameter � 3�14� in. 14. diameter � 15.6 cm

15. radius � 1.1 in. 16. diameter � 12�34� yd

11.9 ft2.1 mm

22.5 in.

4.7 yd

8 cm4.3 ft

14 in.35 mm

4 yd

1 cm

6MG1.1, 6MG1.2

Find the area of each circle. Use 3.14 for π.Round to the nearest tenth if necessary.

1. 2. 3.

4. 5. 6.

7. diameter � 9.4 mm 8. diameter � 3�12

�ft 9. radius � 6�14

�in.

10. radius � 4�34

� yd 11. diameter � 15�12

� mi 12. radius � 7.9 km

Estimate to find the approximate area of each circle.

13. 14. 15.

16. SPOTLIGHT A spotlight can be adjusted to effectively light a circular areaof up to 6 meters in diameter. To the nearest tenth, what is the maximumarea that can be effectively lit by the spotlight?

17. ARCHERY The bull’s eye on an archery target has a radius of 3 inches. Theentire target has a radius of 9 inches.To the nearest tenth, find the area ofthe target outside of the bull’s eye.

3 in.

9 in.

14 cm6.1 m

3.8 yd

5.6 cm10 yd4 in.

13 km12 ft7.1 m

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeArea of Circles


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeArea of Circles


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1. POOLS Susan designed a circular poolwith a diameter of 25 meters. What isthe area of the bottom of the pool?Round to the nearest tenth.

2. MONEY Find the area of the coin to thenearest tenth.

19 mm

3. DRUMS What is the area of thedrumhead on the drum shown below?Round to the nearest tenth.

14 in.

4. PIZZA Estimate the area of the top of around pizza that has a diameter of16 inches. Round to the nearest tenth.

5. GARDENING Jane needs to buy mulchfor the garden with the dimensionsshown in the figure. For how much areadoes Jane need to buy mulch? Round tothe nearest tenth.

5.5 yd

6. UTILITIES What is the area of the topsurface of a circular manhole cover thathas a radius of 30 centimeters? Use3.14 for �.

6MG1.1, 6MG1.2

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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Seki KowaJapanese mathematician Seki Kowa (c. 1642–1708) is called The Arithmetical Sage because of his many contributions to the development of mathematics in Japan. Before Seki, mathematics in Japan was considered a form of art to be enjoyed by intellectuals in their leisure time. Seki demonstrated the practical uses of mathematics and introduced social reforms that made it possible for anyone, not just intellectuals, to study mathematics.

One of Seki’s contributions to mathematics was his calculation of a valueof � that was correct to eighteen decimal places.

� � 3.141592653589793238…

Seki had noticed the phenomenon that you see at the right: as thenumber of sides of a regular polygon increases, the polygon looksmore and more like a circle. So, Seki calculated the following ratiofor polygons of increasingly many sides.

As the number of sides of the polygon gets larger, this ratio must getcloser to the ratio of the circumference of the circle to the diameter ofthe circle. This ratio, of course, is �.

You are given information below about a regular polygon and thecircle drawn around the polygon. Use a calculator to find Seki’sratio. (Give as many decimal places as there are in your calculator display.) What do you notice about your answers?

1. length of one side � 5 2. length of one side � 4.5922number of sides � 6 number of sides � 8diameter of circle � 10 diameter of circle � 12

3. length of one side � 3.7544 4. length of one side � 37.5443number of sides � 20 number of sides � 20diameter of circle � 24 diameter of circle � 240

5. length of one side � 1.6754 6. length of one side � 2.6389number of sides � 150 number of sides � 500diameter of circle � 80 diameter of circle � 420

perimeter of regular polygon��diameter of circle drawn around the polygon

6MG1.1, 6MG1.2

Exercises

SPORTS West High School wants to paint field blue, but not the center. Thediagram below shows the dimensions ofthe field and center circle. How mucharea will they need to paint blue?

1. FRAMES Joan wants to paint her favorite picture frame. How much paint would she need to use inorder to cover just the frame?

2. WALLPAPER Richard wants to wallpaper one wall of his bathroom. He has two semi-circular windows along the wall. How much wallpaper must he purchase?

12 ft

8 ft

2 ft 2 ft

10 in.

10 in.

3 in.

3 in.

100 ft

75 ft 30 ft

NAME ________________________________________ DATE ______________ PERIOD _____


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When problem solving, sometimes it is easier to solve a simpler problem first to findthe correct strategy for solving a more difficult problem.

Explore You know that the field is one large rectangle and the center symbol is alarge circle.

Plan You can find the area of the rectangle and the area of the circle andsubtract.

Solve Area of rectangle: A � � wA � 100 � 75 or 7500

Area if circle: A � �r2

A � 3.14 � 152 or 706.5

Subtract: 7500 � 706.5 or 6793.5 ft2

So, they would need to paint 6,793.5 square feet of field.

Check Use estimation to check. The area of the entire field is 7,500 ft and thecircle is approximately 700 feet so the area should be less than 6,800 feet.Since 6,793.5 is less than 6,800 ft, the answer is reasonable.

Example

6MR1.3, 6MR2.2, 6NS2.1Study Guide and InterventionProblem-Solving Investigation: Solve a Simpler Problem

NAME ________________________________________ DATE ______________ PERIOD _____


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Solve a simpler problem to solve.

1. POOL Find the area of the sidewalk around the pool shown below.

2. GEOMETRY Find the area of the shape shown.

3. POPULATION The population of Ghostown, USA is decreasing at a rate of3 people per year. If there are currently 831 people living in the town,when will the town be deserted?

4. STAINED GLASS Find the area of the stained glass window shown below.Use 3.14 for π. Round to the nearest hundredth if necessary.

5. STOVETOPS What is the area of the stovetop shown, not including theburners? Use 3.14 for π. Round to the nearest hundredth if necessary.

6. POOLS Water is being added at a rate of 50 gallons per minute to a pool.How long will it take until the 10,000 gallon pool is full?

3 ft 0.75 ft

2 ft

1.6 in.

1.6 in.

3 cm

8 cm

8 cm

2 cm

2 ft

60 ft 30 ft 2 ft

6MR1.3, 6MR2.2, 6NS2.1Skills PracticeProblem-Solving Investigation: Solve a Simpler Problem

Select the Operation

Mixed Problem Solving

NAME ________________________________________ DATE ______________ PERIOD _____


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Solve Exercises 1 and 2. Use the solve asimpler problem strategy.

1. STADIUM The exits in a stadium aredesigned to allow 1,200 people to leavethe stadium each minute. At this rate,how long would it take for 10,800 peopleto leave the stadium?

2. PHARMACY A city has three majorpharmacy chains which have a total of895,000 customers. Approximately howmany customers do business at eachmajor pharmacy?

Use any strategy to solve Exercises 3and 4. Some strategies are shown below.

3. CARPENTRY Mr. Fernandez uses 7boards that are 4 feet long and 6 incheswide to make one bookshelf. If he buyslumber in lengths of 8 feet with a widthof 12 inches, how many pieces of lumberdoes he need to purchase to make 5bookshelves?

4. AREA Stacey is making a stained glasswindow above her front doorway in theshape as shown in the figure. To thenearest tenth, what is the area of theshaded portion of the window?

For Exercises 5 and 6, select theappropriate operation(s) to solve theproblems. Justify your selection(s) andsolve the problem.

5. QUALITY CONTROL For every 250televisions tested, 3 televisions arefound to be defective. How manytelevisions were tested if 48 televisionswere found defective?

6. APPLIANCE REPAIR An appliance repaircompany charged $35 to make a housecall. After arriving, the companycharged $10 for every 15 minutes oflabor. How much was the repair bill ifthe new parts cost $23 and theappliance took 45 minutes to repair?

3 ft

1 ft

Pharmacy PercentA 54.8%B 32.4%C 12.8%

PROBLEM-SOLVING STRATEGIES• Use the four-step plan.• Eliminate possibilities.• Draw a diagram.• Solve a simpler problem.

6MR1.3, 6MR2.2, 6NS2.1PracticeProblem-Solving Investigation: Solve a Simpler Problem

Solve each problem using any strategy you have learned.

NAME ________________________________________ DATE ______________ PERIOD _____


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1. AREA Find the area of the figure below.Use 3.14 for π.

8 in.

4 in.

2. MONEY The table below shows theamount of money Shoshi earned forworking various hours. Write a rule torepresent the amount of pay, P, basedon the number of hours worked, h.

3. SALES For every nickel increase inprice, the subscriptions to thePerrysville Paper decreases by 5 people.If 1,256 people currently subscribe tothe Paper, how many people willsubscribe to it if the price is increasedby $0.25?

4. SCALE DRAWING Shannon is creating ascale drawing of her classroom. If she is

using the scale 1 foot � �12

� inch and the

room model is 10 inches by 15 inches,what are the dimensions of the actualroom?

5. STUDY TIME The circle graph belowshows the results to a survey askingstudents how long they study eachnight. In a school of 400 students, howmany students study 1.5 – 2.5 hoursper night?

3–4 hours10%

1.5–2.5 hours65%

0–1 hours65%

6. PHOTOGRAPHY What is the area of thematte pictured below?

1.5 in.

4 in.

6 in.

1.5 in.

7. TRAVEL How far has Kim traveled ifshe has driven 45 miles per hour for 4hours?

8. SISTERS Angela is 3 years older thanSusie. Becca is 2 years younger thanSusie. If Becca is 10 years old, how oldare Susie and Angela?

Hours 1 2 3Pay 5.50 11.00 16.50

6MR1.3, 6MR2.2, 6NS2.1Word Problem PracticeProblem-Solving Investigation: Solve a Simpler Problem

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideArea of Complex Figures


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Get Ready for the LessonRead the introduction at the top of page 596 in your textbook. Writeyour answers below.

1. Describe the shape of the kitchen.

2. How could you determine the area of the kitchen?

3. How could you determine the total square footage of a house with rooms shapedlike these?

Read the Lesson4. Look up the term footage in a dictionary. Write the meaning that matches

the way the term is used in this lesson.

5. What do you think the term square footage means?

6. Which word of the compound square footage indicates area? Explain.

7. Look up the term two-dimensional in a dictionary.

8. Name two dimensions of each of the following figures.

a. rectangle b. parallelogram c. triangle

9. Refer to the figure in Example 1. How do you know that the base of the triangleis 4 inches long?

Remember What You Learned10. Look in a dictionary for the meanings of the word complex when used as

an adjective. Write the meaning of the word as it is used in this lesson.Why can the figures in Examples 1 and 2 be considered complex figures?

6AF3.1, 6AF3.2

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionArea of Complex Figures


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Find the area of the figure at the rightin square feet.

The figure can be separated into a rectangle and a trapezoid. Find the area of each.

Area of Rectangle

A � �w Area of a rectangle

A � 12 � 8 Replace � with 12 and w with 8.

A � 96 Multiply.

Area of Trapezoid

A � �12�h(b1 � b2) Area of a trapezoid

A � �12�(4)(4 � 12) Replace h with 4, b1 with 4, and b2 with 12.

A � 32 Multiply.

The area of the figure is 96 � 32 or 128 square feet.

Find the area of each figure. Use 3.14 for �. Round to the nearesttenth if necessary.

1. 2.

3. 18 mm

38 mm

11 mm

4 in. 5 in.

4 cm

6.5 cm

13 cm

6 cm

6 cm

12 ft

4 ft

4 ft

12 ft

8 ft

12 ft

4 ft

4 ft

8 ft

Complex figures are made of triangles, quadrilaterals, semicircles, and other two-dimensional figures.To find the area of a complex figure, separate it into figures whose areas you know how to find, andthen add the areas.

Example 1

6AF3.1, 6AF3.2

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeArea of Complex Figures


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1. 2.

3. 4.

5. 6.

7. 8.1.3 ft

1.3 ft

3.5 ft

3.5 ft

3.5 ft

3.5 ft4 m

4 m

2 m

2 m

2 m

20 yd

9 yd11 yd

9 yd

4 yd 4 yd

13 m

9 m

7 m

3 in. 4 in.

9 in.15 in.

5 in.

10 in.

30 in.

15 in.

7 mm5 mm

6 mm

7 cm

7 cm

6AF3.1, 6AF3.2


1. 2. 3.

4. 5. 6.

In each diagram below, one square unit represents 5 square meters.Find the area of each figure.

7. 8.

9. AUDITORIUM The diagram at the right gives the dimensions of an auditorium. If new carpet is needed for the auditorium, what will be the area of the carpet? Round to the nearest square yard.

SIDING For Exercises 10 and 11, use the diagram that shows one end of a cottage.

10. Each end of the cottage needs new siding. Findthe total area that needs new siding.

11. The siding material costs $75 for a bundle of siding that covers an area of 100 squarefeet. What will be the total cost to put siding on both ends of the cottage? Justify youranswer.

8.5 ft

28 ft

12.5 ft

40 yd

65 yd

55 yd

6.5 m

3.2 m

1.8 m

4.5 m

4.5 m 4.5 m

22 cm

12 cm

8 cm 9 cm12 yd

10 yd

3 mm

9.3 mm

7.8 mm

5.5 ft

6 ft

8 ft

4 in.

6 in.

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeArea of Complex Figures


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeArea of Complex Figures


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11-6

ARCHITECTURE For Exercises 1–6 use Jaco’spreliminary design of his vacation house at the right. Round to the nearest tenth ifnecessary.

8 ft4 ft

4 ft

4 ft

8 ft 4 ft

4 ft

4 ft

8 ft

8 ft 4 ft4 ft

2 ft

4 ft12 ft 4 ft

12 ft

16 ft

16 ft12 ft

16 ft

16 ft

4 ft 4 ft

bedroom1

kitchen bedroom2

bathroom

livingroomden

1. What type of figure is bedroom 1? Findthe area of bedroom 1.

2. What is the area of the bedroom 2?What figures did you use to find thearea?

3. What is the area of the bathroom?What are the dimensions of the figuresyou used to find this area?

4. What is the area of the living room?How many figures did you use to findthis area?

5. What is the area of the den? Whatwould the area of the den be if thesemicircular window were removed andreplaced with a flat window?

6. What is the area of the kitchen? If Jacoadds a rectangular cooking island inthe middle of the kitchen withdimensions 6 feet by 4 feet, how manysquare feet of space will be left?

6AF3.1, 6AF3.2

NAME ________________________________________ DATE ______________ PERIOD _____

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Extending the Pythagorean TheoremThe Pythagorean Theorem says that the sum of the areas of thetwo smaller squares is equal to the area of the largest square.Show that the Pythagorean Theorem can be extended to includeother shapes on the sides of a triangle. To do so, find the areas ofthe two smaller shapes. Then, check that their sum equals thearea of the largest shape. Round each answer to the nearest tenth.

1. area of smallest shape: 2. area of smallest shape:

area of middle shape: area of middle shape:

area of largest shape: area of largest shape:

3. area of smallest shape: 4. area of smallest shape:

area of middle shape: area of middle shape:

area of largest shape: area of largest shape:

3 in.1.5 in.1.5 in.

5 in.

2.5 in.

2.5 in.

4 in.

2 in.

2 in.

3 in.

3 in.

5 in.5 in.

4 in.

4 in.

1.5in. 3 in. 5 in.

4 in.

2.5 in.

2 in.

5 in.

4 in.

3 in.

55

44 3

3

7MG3.3


1. Study the shape of each object. Then compare and contrast the propertiesof each object.

Read the LessonFill in the blanks.

2. The top and bottom faces of a prism are _______________ and are

_______________.

3. The shape of the base tells the name of the _______________.

4. The base of a cone is a _______________.

5. A _______________ has no faces, bases, edges, or vertices.

6. The bases of a cylinder are _______________.

7. All of the points on a _______________ are the same distance from the

_______________.

Remember What You Learned8. Compare and contrast a triangular prism, a triangular pyramid, and a

cone.

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideThree Dimensional Figures


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Exercises

For each figure, name the shape of the base(s). Then classify eachfigure.

A. B.

For each figure name the shape of the base(s). Then classify eachfigure.

1. 2.

3. 4.

5. 6.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionThree Dimensional Figures


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Prisms At least 3 rectangular Top and bottom bases Shape of the base tellslateral faces are parallel the name of the prism

Pyramids At least three One base shaped like Shape of the base tells triangular lateral faces any 3-sided closed figure the name of the pyramid

Cones Only one base Base is a circle One vertex and no edges

Cylinders Only two bases Bases are circles No vertices and no edges

Spheres All points are the same No faces or bases No edges or verticesdistance from the center

Example

7MG3.6

The figure has twoparallel triangularbases and threerectangular faces.The figure is atriangular prism.

The figure has twocircular bases andno edges.The figure is acylinder.

For each figure, identify the shape of the base(s). Then classify thefigure.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeThree-Dimensional Figures


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For each figure, identify the shape of the base(s), if any. Then classifythe figure.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. CANDLES What three-dimensional figure describes the candle shown?

11. FENCES The basic shape of a fence post is made of twogeometric figures. Classify these figures.

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeThree-Dimensional Figures


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeThree-Dimensional Figures


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1. SPORTS A regulation basketball weighs20-22 ounces. Classify the shape of aregulation basketball as a three-dimensional figure.

2. ICE CREAM The picture shows an icecream cone with a single scoop on top.What two three-dimensional shapesmake up the ice cream and cone?

3. SHIPPING Jessie bought a box to shipher gifts to her grandmother. Classifythe shape of a box as a three-dimensional figure.

4. LAUNDRY Classify the shape of a the laundry hamper shown as a three-dimensional figure.

5. SCHOOL PROJECT Jarnel is creating adiorama for his class project. He plansto use a shoebox to build the diorama.Classify the shape of a shoebox as athree-dimensional figure.

6. SOUP Classify the shape of a soup canas a three-dimensional figure.

7. BABY BLOCKS Classify the shape of thebaby block as a three-dimensionalfigure.

8. EARTH Classify the shape of the Earthas a three-dimensional figure.

7MG3.6

Properties of PrismsLeonard Euler, born in 1707, was one of the world’s greatest mathematicians. One of hisaccomplishments was discovering a formula for calculating the number of faces, edges, andvertices on a three-dimensional figure. He found that V � F � E � 2. (Vertices � Faces �Edges � 2)

A triangular prism has 6 vertices, 5 faces, and 9 edges. It hasthe fewest faces, edges, and vertices of any prism.

1. Complete the table for a hexagonal and an octagonal prism.

2. If a prism has 14 vertices and 21 edges, how many faces does it have?Use Euler’s formula.

3. A prism has 20 vertices. How many faces does it have? How many edges?

4. An “n-gonal” prism has two bases, each with n sides. Use the patterns inthe table to write expressions to find the number of faces, edges, andvertices and n-gonal prism has.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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Prism Vertices Faces Edges

triangular 6 5 9

rectangular 8 6 12

pentagonal 10 7 15

hexagonal

octagonal

7MG3.6

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideDrawing Three-Dimensional Figures


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11-8

Get Ready for the LessonRead the introduction at the top of page 608 in your textbook.Write your answers below.

1. Which view of the Washington monument is shown in the comic?

2. Find a photograph of the Washington Monument and draw a side view.

Read the Lesson3. A two-dimensional figure has two dimensions. What are they?

4. A three-dimensional figure has three dimensions. What are they?

5. Label the dimensions of each figure.

6. Underline the word that makes the sentence true.A (rectangle, cube) is a three-dimensional figure.

Remember What You Learned7. Make models of a two-dimensional figure and a three-dimensional figure.

Use any material you like—for example, paper, cardboard, toothpicks,gumdrops.

5MG2.3, 6MR2.4

Example 1

Example 2

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____


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Draw a top, a side, and a front view of the solid at the right.

The top view is a triangle. The side and front views are rectangles.

top side front

Draw the solid using the top, side, and front views shown below.

top side front

Step 1 Use the top view to draw the base of the figure, a 1-by-3 rectangle.

Step 2 Add edges to make the base a solid figure.

Step 3 Use the side and front views to complete the figure.

1. Draw a top, a side, and front view of the solid.

2. Draw the solid whose top, side, and front views are shown. Use isometric dot paper.

top side front

side

front

top

front

top

side

A solid is a three-dimensional figure.

5MG2.3, 6MR2.4Study Guide and InterventionDrawing Three-Dimensional Figures

NAME ________________________________________ DATE ______________ PERIOD _____


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Draw a top, a side, and a front view of each solid.

1.

2.

3.

Draw each solid using the top, side, and front views shown. Useisometric dot paper.

4.

5. top side front

top side front

5MG2.3, 6MR2.4Skills PracticeDrawing Three-Dimensional Figures


1. 2.

3. 4.

Draw each solid whose top, side, and front views are shown. Useisometric dot paper.

1. 2.

7. HAT RACK Draw a top, a side, and a front view of the hat rack shown.

8. MUSIC Sketch views of the top,side, and front of the piano shown.

front side top front side top

NAME ________________________________________ DATE ______________ PERIOD _____


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Drawing Three-Dimensional Figures

NAME ________________________________________ DATE ______________ PERIOD _____


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11-8

1. ARCHITECTURE The Transamerica Pyramid, builtfrom 1969 to 1972, towersabove the San Franciscoskyline.

Draw the top, side, and frontviews of the Transamericabuilding.

2. MONUMENTS Since its completion in1965, Eero Saarinen’s 630-foot GatewayArch has stood above St. Louis.

Draw the top, side, and front views ofthe Gateway Arch.

3. GRAPHICS Dan is creating a computer-generated image of a coffee cup. To dothis, he needs to enter the top, side, andfront views of the cup. Draw the viewsthat Dan should enter.

4. HISTORY The Mausoleum atHalicarnassus is one of the SevenWonders of the Ancient World. Draw atop view, a side view, and a front viewof the mausoleum without the chariotstatue at the top.

5MG2.3, 6MR2.4Word Problem PracticeDrawing Three-Dimensional Figures

NAME ________________________________________ DATE ______________ PERIOD _____

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Counting CubesThe figures on this page have been built by gluing cubes together. Use yourvisual imagination to count the total number of cubes as well as the numberof cubes with glue on 1, 2, 3, 4, or 5, or 6 faces.

Complete this chart for the figures below.

1. 2. 3.

4. 5. 6.

Total Number of Faces with Glue on ThemFigure Number

of Cubes 1 face 2 faces 3 faces 4 faces 5 faces 6 faces

1

2

3

4

5

6

5MG2.3, 6MR2.4

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading Guide Volume of Prisms


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11-9


1. What is the area of the base, or bottom, of the box? What is the height ofthe box?

2. How many centimeter cubes fit in the box?

3. What do you notice about the product of the base area and the height ofthe box?

Read the Lesson4. Which of the figures at the right is a

rectangular prism? Why is the other figure not a rectangular prism?

Remember What You Learned5. Tell how to find the volume of a rectangular prism in words.

A B

6MG1.3

Example

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionVolume of Prisms


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Find the volume of the rectangular prism.

V � �wh Volume of a rectangular prism

V � 5 � 6 � 8 Replace � with 5, w with 6, and h with 8.

V � 240 Multiply.

The volume is 240 cubic inches.

Find the volume of each rectangular prism. Round to the nearesttenth if necessary.

1. 2. 3.

3 ft

2 ft2.7 ft

10 cm7 cm

9 cm

4 m

3 m

7 m

6 in.

5 in.

8 in.

The volume of a three-dimensional figure is the measure of space occupied by it. It is measured in cubic units such ascubic centimeters (cm3) or cubic inches (in3). The volume of the figure at the right can be shown using cubes.

The bottom layer, There are or base, has 4 � 3 } two layers.or 12 cubes.

It takes 12 � 2 or 24 cubes to fill the box. So, the volume of the box is 24 cubic meters.

A rectangular prism is a three-dimensional figure that has two parallel and congruent sides, or bases,that are rectangles. To find the volume of a rectangular prism, multiply the area of the base and theheight, or find the product of the length �, the width w, and the height h.

V � Bh or V � �wh

4 m

2 m

3 m

➝➝

6MG1.3

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeVolume of Prisms


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11-9

Find the volume of each rectangular prism. Round to the nearesttenth if necessary.

1. 2. 3.

4. 5. 6.

7. 8. 9.

4.5 cm

1.2 cm1.5 cm

9.6 in.

4.8 in.

15 in.4 ft

4 ft34

2 ft12

9 cm

7.2 cm3 cm7 in.

2.8 in.

9.5 in.

3 mm 5 mm

12 mm

4 m

4 m6 m6 in.

10 in.

5 in.

7 cm3 cm

3 cm

6MG1.3

Find the volume of each prism. Round to the nearest tenth ifnecessary.

1. 2. 3.

4. 5. 6.

7. 8. 9.

ESTIMATION Estimate to find the approximate volume of each prism.

10. 11.

12. ALGEBRA The base of a rectangular prism has an area of 15.3 square inches and avolume of 185.13 cubic inches. Write an equation that can be used to find the height hof the prism. Then find the height of the prism.

13. MAIL The United States Post Office has two different priority mail flat rate boxes.

Which box has the greater volume? Justify your answer. Box 1: 6�12� in. � 8�

12� in. � 11 in.

Box 2: 3�38� in. � 11�

78� in. � 13�

58� in.

4.8 m

5.9 m

6.1 m

6 yd78

4 yd14

3 yd18

1 in.12

1 in.12

1 in.12

4 ft

2 ft12

3 ft12

8 yd5 yd1

2

7 yd34

2.6 m5.1 m

4.1 m

4 yd

3 yd 5 yd1.1 mm

2.6 mm

1.5 mm

4.2 ft2 ft

3.5 ft6 m

8 m

12 m

10 in.

5 in.7 in.

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeVolume of Prisms


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NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeVolume of Prisms


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11-9

1. PACKAGING A cereal box has a length of

8 inches, a width of 1�34� inches, and a

height of 12�18� inches. What is the

volume of the cereal box?

2. FOOD STORAGE Nara wants todetermine how much ice it will take tofill her cooler. If the cooler has a lengthof 22 inches, a width of 12 inches, and a

height of 10�12� inches, how much ice will

her cooler hold?

3. TRANSPORTATION The cargo-carryingpart of Billy’s truck has a length of8.3 meters, a width of 3 meters, and aheight of 4.2 meters. What is themaximum volume of sand that Billy’struck can carry?

4. PLUMBING Alexia’s bathroom has a tubin the shape of a rectangular prismwith a length of 1.5 meters, a width of0.5 meter, and a height of 0.4 meter.How many cubic feet of water can ithold?

5. PACKAGING A box of tissues has alength of 11.2 centimeters, a width of11.2 centimeters, and a height of13 centimeters. What is the volume ofthe tissue box?

6. GEOMETRY A pentagonal prism is aprism that has bases that arepentagons. Use V � Bh where B is thearea of the base, to find the volume ofthe pentagonal prism below.

4.5 cm

B = 26.3 cm2

6MG1.3

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Volumes of PyramidsA pyramid and a prism with the same base and height are shown below.

The exercises on this page will help you discover how their volumes arerelated.

Enlarge and make copies of the two patterns below to make the openpyramid and the open prism shown above. (Each equilateral triangleshould measure 8 centimeters on a side.)

1. Describe the bases of the two solids.

2. How do the heights of the solids compare?

3. Fill the open pyramid with sand or sugar. Pour the contents into the open prism. How many times must you do this to fill the open prism?

4. Describe how you would find the volume of the pyramid shown at the right.

5. Generalize: State a formula for the volume of a pyramid.

OpenBottom

OpenTop

6MG1.3

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

TI-73 ActivityVolume of Prisms


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11-9

To solve problems involving formulas, you can either use basic arithmetic operations or youcan use the Equation Solver.

Find the volume of this prism. Use the formula V � �wh.

Method A 4.6 2.5 7.1

The answer is 81.65.

Method B

Step 1 Choose Equation Solver.

6

Step 2 Enter the formula after the symbol eqn.

[TEXT] V � L W H Done

Step 3 Enter the values given in the figure: L � 4.6, W � 2.5, H � 7.1

4.6 2.5 7.1

Step 4 Solve for V, the volume.

The volume is 81.65 cubic centimeters.

Find the volume of each rectangular prism to the nearest tenth. Use the sameformula and enter the values for �, w, and h.

1. 2. 3.

4. CHALLENGE Suppose you need a rectangular prism with length 4 inches and width 3.5 inches and a volume of 140 cubic inches. What height must the prism have?

3.29 cm1.74 cm

5.67 cm

15 yd

11 yd

21 yd

1.6 cm0.8 cm

2.7 cm

ENTER

ENTERENTER2nd

MATH

ENTER

Example

4.6 cm2.5 cm

7.1 cm

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideVolume of Cylinders


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1. Estimate the number of centimeter cubes that would fit at the bottom ofthe can. Include parts of cubes.

2. How many layers would it take to fill the cylinder?

3. MAKE A CONJECTURE about how you can find the volume of the soup can.

Reading the Lesson4. Write C if the phrase is true of a cylinder, P if the phrase is true of a

prism, or CP if the phrase is true of both.

has bases that are parallel and congruent

has sides and bases that are polygons

has bases that are circular

is a solid

has volume

is three-dimensional

5. What shape is the base of a cylinder?

6. What is the formula for the area of the base of a cylinder?

Remember What You Learned7. Work with a partner. Bring an object that is a cylinder to school. Take the

measurements and determine the volume of your cylindrical object.Exchange objects with your partner, but do not share the calculations.Determine the volume of your partner’s object. Then compare your resultswith those of your partner.

6MG1.3

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionVolume of Cylinders


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11-10

Find the volume of the cylinder. Use 3.14 for π.Round to the nearest tenth.

V � �r2h Volume of a cylinder

V � 3.14(2)2(5) Replace � with 3.14, r with 2, and h with 5.

V � 62.8 Simplify.

The volume is approximately 62.8 cubic inches. Check by using estimation.

Find the volume of each cylinder. Use 3.14 for π.Round to the nearest tenth.

1. 2. 3.

4. radius � 9.5 yd 5. diameter � 6 cm 6. diameter � 3�25

� mheight � 2.2 yd height � 11 cm

height � 1�14� m

2 in.

2 in.

4 ft

12.9 ft

10 mm

18 mm

2 in.

5 in.

As with prisms, the area of the base of a cylinder tells the number of cubic units in one layer. Theheight tells how many layers there are in the cylinder. The volume V of a cylinder with radius r is thearea of the base B times the height h.

V � Bh or V = �r 2h, where B � �r 2

r

h

B = �r2

Example

6MG1.3

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeVolume of Cylinders


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1. 2. 3.

4. 5. 6.

7. radius � 8.8 cm 8. radius � 4 ft

height � 4.7 cm height � 2�12� ft

9. diameter � 10 mm 10. diameter � 7.1 in.height � 4 mm height � 1 in.

1.9 in.

6.2 in.

5.3 m

8.7 m

3 yd

6 yd

12

12 in. 4 in.8 ft

9 ft

7 cm

20 cm

6MG1.3


1. 2. 3.

4. 5. 6.

7. radius � 3.7 cm 8. diameter � 6 in. 9. radius � 5�14

� yd

height � 5.2 cm height � 4�12

� in height � 6�12

� yd

10. CONTAINER What is the volume of a barrel that has a diameter of 1�12

� feetand a height of 4 feet?

ESTIMATION Match each cylinder with its approximate volume.

11. diameter � 4 cm, height � 3.6 cm a. 108 ft3

12. radius � 2.7 cm, height � 5 cm b. 135 ft3

13. radius � 3 cm, height � 4.1 cm c. 96 ft3

14. diameter � 8.2 cm, height � 2 cm d. 48 ft3

15. FUEL Two fuel tanks with the dimensions shown have the same volume.What is the value of h?

6 ft

h

8 ft

3 ft

4.2cm

2.1cm3 mm

12.7 mm8 in.

23 in.

9 yd 4 yd14 m

11 m

10 ft

6 ft

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeVolume of Cylinders


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11-10 6MG1.3

NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeVolume of Cylinders


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1. WATER STORAGE A cylindrical watertank has a diameter of 5.3 meters anda height of 9 meters. What is themaximum volume that the water tankcan hold? Round to the nearest tenth.

2. PACKAGING A can of corn has adiameter of 6.6 centimeters and aheight of 9.9 centimeters. How muchcorn can the can hold? Round to thenearest tenth.

3. CONTAINERS Tionna wants to determinethe maximum capacity of a cylindricalbucket that has a radius of 6 inchesand a height of 12 inches. What is thecapacity of Tionna’s bucket? Round tothe nearest tenth.

4. DESIGN Rodolfo is designing a new,cylindrical drinking glass. If the glasshas a diameter of 8 centimeters and aheight of 12.8 centimeters, what is itsvolume? Round to the nearest tenth.

5. PAINT A can of paint is 15 centimetershigh and has a diameter of 13.6 cm.What is the volume of the can? Roundto the nearest tenth.

6. SPICES A spice manufacturer uses acylindrical dispenser like the oneshown. Find the volume of thedispenser to the nearest tenth.

1.7 in.

3 in.

6MG1.3

NAME ________________________________________ DATE ______________ PERIOD _____

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11-10

Volumes of Non-Right SolidsImagine a stack of ten pennies. By pushing against the stack, you can change its shape as shown at the right.But, the volume of the stack does not change.

The diagrams below show prisms and cylinders that have the same volume but do not have the same shape.

Find the volume of each solid figure. Use 3.14 for �. Round to the nearest tenth.

1. 2. 3.

4. 5. 6.

15 cm

4 cm

4 cm10 cm

2 cm

10 yd

5 yd

3 yd

7 yd

6 yd

12 in.

10 in.

5 in.

10 in.

11 in.

2 in.3 in.

2 m

3 m2.5 m

height height height

radiusradius

height

lengthlength

Right Prism Non-right Prism Right Cylinder Non-right Cylinder

width width

6MG1.3

NAME ________________________________________ DATE ______________ PERIOD _____

Student Recording SheetUse this recording sheet with pages 632–633 of the Student Edition.


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11

Read each question. Then fill in thecorrect answer.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Record your answers for Question 12 onthe back of this paper.

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

Pre-AP

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General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she

arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.

• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.

• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.

Exercise 12 Rubric

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


11 Rubric for Scoring Pre-AP(Use to score the Pre-AP question on page 633 of the Student Edition.)

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Score Specific Criteria4 The Pythagorean Theorem is used to determine the height of the parallelogram. An

accurate explanation that the area of the side (60 � 46.5 in2) is greater that the areaof the floor (60 � 30 in2) is given. The area of two triangular regions is correctlydetermined to be 1,320 in2.

3 The correct values are found. However, the explanation is correct but not complete.ORThe explanation is correct and complete, but one computational error is made infinding the height of the parallelogram or the area of the two triangular regions.

2 The Pythagorean Theorem is used to determine the height of the parallelogram, andthe explanation is correct and complete. However, the area of only one triangularregion is found. ORThe Pythagorean Theorem is used to determine the height of the parallelogram, thearea of the side is stated to be greater than the area of the floor, and the area of thetwo triangular regions is correctly determined. However, the explanation is incorrector not given.

1 The area of the two triangular regions is correct, but the answer to Part a iscompletely incorrect. ORThe area of the side is stated to be greater than the area of the floor, but theexplanation is incorrect or not given. The area of the two triangular regions is incorrect.

0 Response is completely incorrect.

Find the area of each parallelogram. Round to the nearest tenth if necessary.

1. 2. 1.

2.

Find the area of each figure.

3. 4. 3.

4.

5. Find the circumference of the circle. 5.Use 3.14 for π.Round to the nearest tenth.

30 ft

20 ft

68 ft

18 ft64 m

80 m

120 m

39 ft

24 ft17 ft8.9 m

4.3 m

Find the area of each figure. Use 3.14 for π. Round to the nearest tenth.

1. 2. 1.

2.

3.

3. radius � 4 in. 4. diameter � 12 mm 4.

5. MULTIPLE CHOICE Mason can make 5 picture frames in 2 hours. How many picture frames can 4 people make in 8 hours working at the same rate?

A. 20 B. 40 C. 80 D. 160 5.


Chapter 11 Quiz 1(Lessons 11-1 and 11-3)


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NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

11

11

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5 mm

3.6 cm

9.5 ft

3 ft5 ft

4 ft

3.4 ft


1. 2. 1.

2.

3. Classify the figure at the right. 3.

Draw a top, a side, and a front view of each solid. 4.

4. 5.

5.

5 ft

9 ft

Find the volume of each rectangular prism.

1. 2.

1.

2.


3. 4. 3.

4.

5. Find the volume of a cylinder-shaped oatmeal carton 5.that has a radius of 5�

12� inches and a height of 10 inches.

Round to the nearest tenth.

20 cm

13 cm

4 yd17 yd

4 mm22 mm

25 mm

16 ft

16.2 ft

2 ft




NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

11

11 Copyright ©

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3 in.

4 in.

5 in.

1. Find the circumference of a circle with radius 6�14� meters. Round

to the nearest tenth.

A. 9.8 m B. 19.6 m C. 39.3 m D. 122.7 m 1.

2. Find the area of the parallelogram.

F. 72 in2 H. 36 in2

G. 70 in2 J. 18 in2 2.

3. What is the area of a triangle with a base of 24.7 centimeters and a height of 15.2 centimeters?

A. 39.9 cm2 B. 93.85 cm2 C. 187.7 cm2 D. 375.44 cm2 3.

4. Find the area of the circle. Round to the nearest tenth.

F. 1,661.9 yd2 H. 72.3 ydG. 415.3 yd2 J. 36.1 yd2 4.

5. TABLES A circular table has a radius of 16 inches.What is the area of the table?

A. 100.5 in2 B. 201.1 in2 C. 803.8 in2 D. 3,216.0 in2 5.

Find the area of each figure.

6. 7. 6.

7.

Find the circumference of each circle. Use 3.14 for �.Round to the nearest tenth if necessary.

8. radius � 8.9 cm 8.

9. diameter � 4�12� yd 9.

10. Find the area of the figure.Round to the nearest tenth if necessary. 10.

12 in.

6 in.

Chapter 11 Mid-Chapter Test(Lessons 11-1 and 11-3)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____11


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23 yd

6 cm

11 cm

9.5 ft

3 ft5 ft

4 ft

3.4 ft

7 cm

10 cm

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NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


11 Chapter 11 Vocabulary Test

Write the letter of the term that best matches each statement or phrase. Someterms may be used more than once.

1. any three-dimensional figure

2. the distance across a circle through the center

3. the distance around a circle

4. solid figure that has two parallel and congruent bases that are rectangles

5. the measures of space occupied by a solid

6. The expression 2�r is used to find this measure.

7. the distance from the center of a circle to any point on the circle

8. solid figure that has no vertices and no edges

9. solid figure that has only one base

10. solid figure that has two congruent, parallel circles as bases

Define the term in your own words.

11. complex figures

12. lateral face

base

center

circle

circumference

complex figure

cone

cylinder

diameter

edge

face

height

lateral face

prism

pyramid

radius

rectangular prism

solid

sphere

three-dimensional figure

triangular prism

vertex

volume

a. rectangular prism

b. volume

c. cylinder

d. pyramid

e. diameter

f. solid

g. circumference

h. radius

Write the letter for the correct answer in the blank at the right of eachquestion.

1. POOLS A rectangular pool is 6 feet long by 4 feet wide and 6 inches deep. What is the volume of the pool?A. 12 ft3 B. 144 ft3 C. 168 ft3 D. 296 ft3 1.

2. What is the area of a parallelogram with a height of 4 yards and a baseof 5 yards?F. 80 yd2 G. 20 yd2 H. 10 yd2 J. �

45� yd2 2.

3. GARDENS Find the area of a circular garden with a radius of 6 feet.Round to the nearest tenth.A. 18.8 ft2 B. 37.7 ft2 C. 113.0 ft2 D. 452.4 ft2 3.

Find the area of each figure. Round to the nearest tenth if necessary.4.

F. 5,026.5 m2 H. 125.7 m2

G. 1,256.0 m2 J. 62.8 m2 4.

5.A. 47 m2 C. 75 m2

B. 60 m2 D. 165 m2 5.

6.F. 104.5 m2 H. 330 m2

G. 225.5 m2 J. 660 m2 6.

7.A. 2 in2 C. 50 in2

B. 15 in2 D. 500 in2 7.

8.F. 56 m2 H. 144 m2

G. 104 m2 J. 2,560 m2 8.

Find the circumference of each circle. Use 3.14 for �. Round to the nearest tenth.

9.A. 15.7 ft C. 62.8 ftB. 31.4 ft D. 314 ft 9.

10. radius � 6.7 mmF. 2.1 mm G. 21.0 mm H. 42.1 mm J. 66.1 mm 10.

11. diameter � 15.4 kmA. 48.4 km B. 96.8 km B. 186.3 km D. 745.1 km 11.

10 ft

8 m

8 m

10 m

10 in.

5 in.

41 m

19 m

11 m

8 m

15 m

10 m

40 m

Ass

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11NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 11 Test, Form 1C

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12. Identify the shape of the base of the figure.F. circle H. triangleG. square J. (no base) 12.

13. CONTAINERS Which container has the top, side, and front views given? A. C.

B. D. 13.

14. Find the volume of the rectangular prism.F. 15 m3 H. 142 m3

G. 105 m3 J. 210 m3 14.

15. Find the volume of a rectangular prism with a length of 2.8 centimeters, a width of 1.5 centimeters,and a height of 1.2 centimeters. Round to the nearest tenth.A. 5.0 cm3 B. 9.4 cm3 C. 11.0 cm3 D. 18.7 cm3 15.

16. A cube has 4-inch edges. Find its volume.F. 12 in3 G. 16 in3 H. 64 in3 J. 96 in3 16.

17. Find the volume of the cylinder. Round to the nearest tenth.A. 110.0 in3 C. 296.9 in3

B. 122.5 in3 D. 384.7 in3 17.

18. CANS A can of juice is 6 inches high, and its base has a radius of 2 inches. Find the volume of the can. Round to the nearest tenth.F. 37.7 in3 G. 75.4 in3 H. 100.5 in3 J. 118.4 in3 18.

19. Find the volume of the cylinder. Round to the nearest tenth.A. 1,809.6 yd3 C. 326.7 yd3

B. 452.2 yd3 D. 226.2 yd3 19.

20. Classify the figure.F. circular pyramid H. cylinderG. circular prism J. rectangular prism 20.

Bonus The base of a rectangular prism has an area of B:12.6 square meters. Find the height if the volume is 119.7 cubic meters.

3.5 in.

10 in.

NAME ________________________________________ DATE ______________ PERIOD _____


11 Chapter 11 Test, Form 1 (continued)C

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3 m

5 m

7 m

8 yd9 yd

Write the letter for the correct answer in the blank at the right of eachquestion.

1. PONDS A rectangular pond is 5�12

� feet long, 4�34

� feet wide,and 18 inches deep. What is the volume of the pool? A. 28.25 ft3 B. 39.2 ft3 C. 360 ft3 D. 470.25 ft3 1.

2. What is the area of a parallelogram with a base of 6 inches and a heightof 8 inches?F. 96 in2 G. 48 in2 H. 24 in2 J. �

34� in2 2.

3. GARDENS Find the area of a circle with a diameter of 24 feet.Round to the nearest tenth.A. 1,808.6 ft2 B. 452.2 ft2 C. 75.4 ft2 D. 37.7 ft2 3.


F. 1,017.9 mm2 H. 56.5 mm2

G. 254.3 mm2 J. 28.3 mm2 4.

5.A. 180 m2 C. 360 m2

B. 225 m2 D. 450 m2 5.

6.F. 48 cm2 H. 96 cm2

G. 60 cm2 J. 120 cm2 6.

7.A. 36 m2 C. 72 m2

B. 54 m2 D. 108 m2 7.

8.F. 116.5 in2 H. 85 in2

G. 74.1 in2 J. 50.1 in2 8.

9. Find the circumference of the circle. Use 3.14 for �.Round to the nearest tenth.A. 25.0 yd C. 88.2 ydB. 44.1 yd D. 176.5 yd 9.

28.1 yd

6 in.

8 in.

4 in.

6 m

12 m

9 m

15 cm

9 cm

5 cm 4 cm

12 m15 m

30 m

9 mm

Ass

essm

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11NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 11 Test, Form 2AC

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10. Which solid has the top, the side, and the front views given?

F. H.

G. J. 10.

11. Find the volume of the rectangular prism.A. 28 cm3 C. 400 cm3

B. 160 cm3 D. 600 cm3 11.

12. Find the volume of a rectangular prism with a length of 9.3 meters, a width of 6.6 meters, and a height of 3.2 meters. Round to the nearest tenth.F. 19.1 m3 G. 112.3 m3 H. 196.4 m3 J. 224.5 m3 12.

13. A cube has 9-inch edges. Find its volume.A. 729 in3 B. 486 in3 C. 81 in3 D. 27 in3 13.

14. Find the volume of the cylinder to the nearest tenth.F. 99 cm3 H. 2,797.7 cm3

G. 621.7 cm3 J. 3,419.5 cm3 14.

15. TEA CUPS A cylindrical tea cup has a height of 70 millimeters, and its base has a radius of 30 millimeters. Find the volume of the tea cup to the nearest tenth.A. 2,100 mm3 B. 6,594.0 mm3 C. 197,820 mm3 D. 461,814.1 mm3 15.

16. Classify the figure.

F. rectangular prism H. triangular prism G. rectangular pyramid J. triangular pyramid 16.

Bonus BATTERIES A 9-volt battery has a volume of B:2,657.34 cubic millimeters. The battery is 22.2 millimeters long and 9 millimeters deep. How wide is the battery?

9 cm

11 cm

top side front

NAME ________________________________________ DATE ______________ PERIOD _____


11 Chapter 11 Test, Form 2A (continued)C

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5 cm

15 cm8 cm

Write the letter for the correct answer in the blank at the right of each question.1. PONDS A rectangular pond is 6�

34

� feet long, 4 feet wide, and 18 inches deep. What is the volume of the pool? A. 27 ft3 B. 40.5 ft3 C. 432 ft3 D. 486 ft3 1.

2. What is the area of a parallelogram with a base of 4 miles and a height of 8 miles?F. �

12� mi2 G. 16 mi2 H. 32 mi2 J. 64 mi2 2.

3. GARDENS Find the area of a circular garden with a radius of 20 yards.Round to the nearest tenth.A. 31.4 yd2 B. 62.8 yd2 C. 314.2 yd2 D. 1,256.0 yd2 3.


F. 10,201.9 m2 H. 179.1 m2

G. 2,550.5 m2 J. 89.5 m2 4.

5.A. 578 cm2 C. 289 cm2

B. 374 cm2 D. 187 cm2 5.

6.F. 735 mm2 H. 367.5 mm2

G. 588 mm2 J. 294 mm2 6.

7.A. 56 m2 C. 28 m2

B. 40 m2 D. 20 m2 7.

8.F. 164.5 cm2 H. 105.1 cm2

G. 89.1 cm2 J. 81.1 cm2 8.

9. Find the circumference of the circle. Use 3.14 for �.Round to the nearest tenth.A. 5.5 m C. 22.0 mB. 11.0 m D. 34.5 m 9.

3.5 m

6 cm4 cm

12 cm

8 cm

5 m

8 m

7 m

29 mm

20 mm

15 mm 12 mm

11 cm17 cm

34 cm

57 m

Ass

essm

ent


11NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 11 Test, Form 2BC

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10. Which solid has the top, the side, and the front views given? F. H.

G. J. 10.

11. Find the volume of the rectangular prism.A. 336 mm3 C. 168 mm3

B. 328 mm3 D. 24 mm3 11.

12. Find the volume of a rectangular prism with a length of 7.8 feet, a width of 4.2 feet, and a height of 5 feet. Round to the nearest tenth.F. 185.5 ft3 G. 163.8 ft3 H. 92.86 ft3 J. 17 ft3 12.

13. A cube has 8-inch edges. Find its volume.A. 64 in3 B. 24 in3 C. 384 in3 D. 512 in3 13.

14. Find the volume of the cylinder to the nearest tenth.F. 34,464.6 cm3 H. 1,230.9 cm3

G. 17,232.3 cm3 J. 392 cm3 14.

15. CANS A cylindrical waste can has a height of 20 inches, and its base has a radius of 10 inches. Find the volume of the waste can to the nearest tenth.A. 12,560 in3 B. 6,280.0 in3 C. 1,885.0 in3 D. 1,570.8 in3 15.

16. Classify the figure.F. rectangular prism H. triangular prism G. rectangular pyramid J. triangular pyramid 16.

Bonus TRUNKS A rectangular trunk has a volume B:of 26,880 cubic inches. The trunk is 4 feet long by 28 inches wide. How deep is the trunk?

28 cm

14 cm

14 mm

4 mm6 mm

top side front

NAME ________________________________________ DATE ______________ PERIOD _____


11 Chapter 11 Test, Form 2B (continued)C

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1. Find the circumference of the circle. Use 3.14 for � and 1.round to the nearest tenth.

2. CIRCUS A circus elephant walked 19 feet crossing the circus 2.ring through its center. What is the circumference of thecircus ring? Use 3.14 for � and round to the nearest tenth.


3. 4. 3.

4.

5. 6. 5.

6.


7. radius � 6 cm 7.

8. 8.

9. CARTONS A cylindrical carton is filled with sand. The 9.height of the carton is 9 inches, and the radius of the base is 2 inches. What is the total volume of the carton?

10. Identify the shape of the base(s) of the figure. Then classify the figure. 10.

34 in.

15 m

20 m16 mi

25 mi

11 mi

8 mm14 mm

27 mm7 ft

8 ft

4 ft

12.8 cm

Ass

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11NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 11 Test, Form 2CC

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11. 11.

12. 12.

Draw each solid using the top, side, and front views shown. Use isometric dot paper.

13. 13.

14. 14.

Find the volume of each solid. Use 3.14 for π.Round to the nearest tenth if necessary.

15. 16. 15.

16.

17. 18. 17.

18.

19. 20. 19.

20.

Bonus STORAGE A storage shed with a flat roof is 4 yards long B:by 3 yards wide by 2�

12� yards tall. A cubic yard is equal

to 27 cubic feet. How many cubic feet of storage space does the shed enclose?

top side front

top side front

5 m

6 m

2 in.

5.4 in.

7.1 in.

27.1 cm

8 cm

10 yd

3 yd

18 mm

5 mm 20 mm6 in.13 in.

5 in.

NAME ________________________________________ DATE ______________ PERIOD _____


11 Chapter 11 Test, Form 2C (continued)C

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1. Find the circumference of the circle. Use 3.14 for � and 1.round to the nearest tenth.

2. PIE The diameter of a blueberry pie is 9�12� inches. What is 2.

the circumference of the pie? Use 3.14 for � and round tothe nearest tenth.

Find the area of each figure. Round to the nearest tenthif necessary.

3. 4. 3.

4.

5. 6. 5.

6.


7. diameter � 7 ft 7.

8. 8.

9. GLASSES A cylindrical glass is 8 inches tall. The radius of 9.the base is 1.5 inches. If the glass is full, how many cubic inches of liquid does it hold? Round to the nearest tenth.


4 in.

8 in.

2.7 mm

14 in.

42 cm

22 cm

18 cm

6 m4 m

9 m

50 mm

25 mm20 mm

Ass

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11NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 11 Test, Form 2DC

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11. 11.

12. 12.


13. 13.

14. 14.


15. 16. 15.

16.

17. 18. 17.

18.

19. 20. 19.

20.

Bonus SWIMMING POOLS A swimming pool is 30 feet long by B:12 feet wide by 4 feet deep. A cubic yard of water is 27 cubic feet. How many cubic yards of water can the pool hold? Round to the nearest tenth.

7 cm

7 cm

70.5 mm

35 mm

22 ft

8 ft

19.5 mm9 mm

36.1 mm

48 in.19 in.

7 in.

14 cm

8 cm

6 cm

top side front

top side front

NAME ________________________________________ DATE ______________ PERIOD _____


11 Chapter 11 Test, Form 2D (continued)C

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1. Find the circumference 1.of the circle. Use 3.14 for � and round to the nearest tenth.

2. BICYCLE A bicycle wheel measures 18 inches across. 2.What is the circumference of the wheel? Use 3.14 for �and round to the nearest tenth.


3. 4. 3.

4.

5. 6. 5.

6.


7. diameter � 100 ft 7.

8. 8.

9. TANKS A cylindrical water tank is 38 meters 9.across and 8 meters high. If the tank is half full, how many cubic meters of water are in the tank? Round to the nearest tenth.


3 yd45

19.3 mA

sses

smen

t


11NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 11 Test, Form 3C

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16 cm

10 cm 24 m

30 m

25 m

6 ft

8 ft

10 ft5 ft

57 cm

20 cm

33 cm


11. 11.

12. 12.


13. 13.

14. 14.


15. 16. 15.

16.

17. 18. 17.

18.

19. 20. 19.

20.

Bonus RECYCLING The surface area of a large cube-shaped B:recycling dumpster is 433.5 square feet. What is the volume of the recycling dumpster? Round to the nearest tenth.

15 in.

8.8 in.

8 mm

15 mm48 mm

top side front

top side front

14 in.

25.8 in.

21.3 cm

15 cm

14.3 m

23.5 m

3 m

15.3 ft

9.9 ft13.6 ft

NAME ________________________________________ DATE ______________ PERIOD _____


11 Chapter 11 Test, Form 3 (continued)C

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Demonstrate your knowledge by giving a clear, concise solution to each problem.Be sure to include all relevant drawings and justify your answers. You may showyour solutions in more than one way or investigate beyond the requirements ofthe problems. If necessary, record your answers on another piece of paper.

1. a. Describe two different ways to represent three-dimensional figures in drawings.b. Draw a top, a side, and a front view of a donut.

c. Draw a three-dimensional figure given the top, side, and front views shown.

d. Draw a three-dimensional figure of your choice. Then draw the top, side, and frontviews of the figure.

2. Explain how the formulas for the volume of a rectangular prism and the volume of a cylinder are similar.

3. Will and Steve want to draw a target for playing darts. Will wants todraw a circle, and Steve wants to draw a rectangle. Neither can have aperimeter or circumference larger than 12 centimeters.

a. Estimate the dimensions of the rectangle and the radius of the circle ifthe circumference and perimeter both equal 12 centimeters.

b. The perimeter of the rectangle equals the circumference of the circle.

The length of the rectangle is 6�12� centimeters and the width is 2�

23�

centimeters. What is the radius of the circle?

top side front

Ass

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11NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 11 Extended-Response Test

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1. Find �25�. (Lesson 10-1)

A �25 B 5 C 12.5 D 625 1.

2. Find 17 � 3�35�. Write in simplest form. (Lesson 5-3)

F 14�35� G 13�

45� H 13�1

70�

J 13��25� 2.

3. Write 4�14� as a percent. (Lesson 6-9)

A 425% B 4.25% C �147�% D 0.0425% 3.

4. Find the sale price to the nearest cent for a CD-ROM that costs $50 and is 15% off. (Lesson 7-7)

F $7.50 G $42.50 H $43.50 J $57.50 4.

5. Find the interest earned for a principal of $200, an interest rate of 10%, and a time period of 2 years. (Lesson 8-7)

A $10 B $20 C $30 D $40 5.

6. COLORING There are 6 different crayons for Elia to use to create a birthday card. If she uses only 4 of these colors one time each, how many ways can she choose the colors? (Lesson 9-5)

F 720 G 360 H 120 J 15 6.

7. Find the missing measure in the triangle.Then classify the triangle as acute, right,or obtuse. (Lesson 10-4)

A 10; acute B 90; right C 90; acute D 270; obtuse 7.

8. Use the graph to describe the movement from �XYZ to �X�Y�Z�.(Lesson 10-9)

F 4 right, up 2 H 3 right, up 2G 3 right, up 3 J 4 right, up 3 8. F G H J

A B C D

32˚

˚x

58˚

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

y

xO

Y'

X'

X

Z'Y

Z

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


11 Standardized Test Practice(Chapters 1–11)

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Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

9. What is the area of a parallelogram that has a base of 24 meters and a height of 16.2 meters? (Lesson 11-1)

A 40.2 m2 B 80.4 m2 C 194.4 m2 D 388.8 m2 9.

10. DINING The tables at Cozy Cafe have a diameter of 4 feet. What is the circumference of a table to the nearest tenth? (Lesson 11-3)

F 6.3 ft G 12.6 ft H 16 ft J 25.1 ft 10.

11. Choose the top, side, and front views of the figure that are drawn correctly. (Lesson 11-8)

A C

B D 11.

12. Find the volume of a rectangular prism with a length of 1.7 meters,a width of 4 meters, and a height of 2.5 meters. (Lesson 11-9)

F 8.2 m3 G 17 m3 H 42.3 m3 J 551.4 m3 12.

13. Find the volume of the cylinder. Round to the nearest tenth. (Lesson 11-10)

A 320 cm3

B 628 cm3

C 653.5 cm3

D 1,004.8 cm3 13.

14. Find the volume of the cylinder. Round to the nearest tenth. (Lesson 11-10)

F 2,671.9 in3

G 10,385.6 in3

H 29,688.1 in3

J 41,542.2 in3 14.

15. Find the percent of change from 14 to 26, to the nearest whole percent. (Lesson 7-8)

A 33 B 46 C 54 D 86 15.

16. What is the area of a trapezoid with bases 8 inches and 12.5 inches, and a height of 6 inches? (Lesson 11-2)

F 75 in2 G 61.5 in2 H 48 in2 J 26.5 in2 16. F G H J

A B C D

F G H J

21 in. 30 in.

A B C D

8 cm

5 cm

F G H J

A B C Dtop side fronttop side front

top side fronttop side front

F G H J

A B C D


Ass

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11NAME ________________________________________ DATE ______________ PERIOD _____

Standardized Test Practice (continued)

(Chapters 1–11)

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17. Write the next three terms of the sequence 17.6, 12, 18, 24, ... (Lesson 1-9)

18. Write 35% as a decimal. (Lesson 4-7) 18.

19. Complete: 2�14� lb � ? oz (Lesson 6-3) 19.

20. Find the interest earned to the nearest cent for

a principal of $97.99, an interest rate of 6�12�%,

and a time period of 3 months. (Lesson 7-8) 20.

21. Draw a top, a side, and a front 21.view of the solid. (Lesson 11-8)

22. Draw the solid using the top, side, and front views shown. Use isometric dot paper. (Lesson 2-8) 22.

Find the volume of the rectangular prism and the cylinder.Round to the nearest tenth if necessary.

23. 24. 23.

24.

25. GARDENING Roxanne is building a flower box that is 10 inches deep by 12 inches wide by 50 inches long. The box does not have a top side so that the flowers can be planted in the box.

a. How many cubic inches of soil will she need if she 25a.fills the box to the top? Show your work. (Lesson 11-9)

b. Suppose she also wants to use a cylindrical flower pot that uses less than half the amount of soil as the box that she built. What are possible dimensions of the pot? Explain. (Lesson 11-10) 25b.

4 yd41 yd

0.7 ft

4.9 ft

3 ft

Part 2: Short Response

Instructions: Write answers to short response in the space provided.

NAME ________________________________________ DATE ______________ PERIOD _____


11 Standardized Test Practice (continued)

(Chapters 1–11)

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gles

,rh

ombu

ses,

and

squ

ares

an

dla

bel

the

base

an

d h

eigh

t fo

r ea

ch.W

rite

th

e fo

rmu

la f

or t

he

area

bel

owea

ch m

odel

.S

ee s

tud

ents

’wo

rk.

3 cm

5 cm

12 c

m

4 51

squ

are

= 1

ft

4

51

squ

are

= 1

ft

4

51

squ

are

= 1

ft

11-1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

6AF

3.1,

6A

F3.

2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Ant

icip

atio

n Gu

ide

Mea

sure

men

t:Tw

o-

and

Th

ree-

Dim

ensi

on

al F

igu

res

Cha

pter

11

7G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Chapter Resources

pygp

Step

2

Step

1

ST

EP

1S

tate

men

tS

TE

P 2

A,D

,or

NS

A o

r D

1.T

he

area

of

a pa

rall

elog

ram

is

the

prod

uct

of

the

len

gth

of

Dit

s ba

se a

nd

the

len

gth

of

its

side

.2.

Th

e ar

ea o

f a

tria

ngl

e ca

n b

e fo

un

d if

th

e le

ngt

h o

f th

e ba

se

Aan

d th

e h

eigh

t is

kn

own

.3.

Th

e ar

ea o

f an

y fi

gure

is

give

n i

n s

quar

e u

nit

s.A

4.T

he

diam

eter

of

a ci

rcle

is

the

dist

ance

fro

m t

he

cen

ter

to

Dan

y po

int

of t

he

circ

le.

5.T

he

circ

um

fere

nce

of

a ci

rcle

equ

als

the

prod

uct

of

�an

d D

r2,w

her

e r

is t

he

radi

us

of t

he

circ

le.

6.A

��

(10)

2is

th

e ar

ea o

f a

circ

le w

ith

a d

iam

eter

of

10 u

nit

s.D

7.T

he

area

of

an i

rreg

ula

r sh

ape

may

be

fou

nd

by s

epar

atin

g th

e sh

ape

into

geo

met

ric

shap

es w

ith

kn

own

are

a fo

rmu

las,

Ath

en f

indi

ng

the

sum

of

the

area

s of

eac

h s

mal

ler

shap

e.8.

A r

ecta

ngu

lar

pris

m h

as 6

fac

es a

nd

8 ve

rtic

es.

A9.

All

th

e fa

ces

of a

pyr

amid

mu

st b

e tr

ian

gles

.D

10.

Th

e to

p vi

ew o

f a

rect

angu

lar

soli

d co

uld

be

a re

ctan

gle

or

Aa

squ

are.

11.

A r

ecta

ngu

lar

pris

m w

ith

a v

olu

me

of 9

0 cu

bic

un

its

cou

ld

Dh

ave

dim

ensi

ons

of 3

,4,a

nd

6 u

nit

s.12

.S

ince

th

e ba

se o

f a

cyli

nde

r is

a c

ircl

e,th

e fo

rmu

la f

or t

he

area

of

a ci

rcle

is

part

of

the

form

ula

for

th

e vo

lum

e of

A

a cy

lin

der.

Bef

ore

you

beg

in C

ha

pte

r 11

•R

ead

each

sta

tem

ent.

•D

ecid

e w

het

her

you

Agr

ee (

A)

or D

isag

ree

(D)

wit

h t

he

stat

emen

t.

•W

rite

A o

r D

in

th

e fi

rst

colu

mn

OR

if

you

are

not

su

re w

het

her

you

agr

ee o

r di

sagr

ee,w

rite

NS

(N

ot S

ure

).

Aft

er y

ou c

omp

lete

Ch

ap

ter

11

•R

erea

d ea

ch s

tate

men

t an

d co

mpl

ete

the

last

col

um

n b

y en

teri

ng

an A

or

a D

.

•D

id a

ny

of y

our

opin

ion

s ab

out

the

stat

emen

ts c

han

ge f

rom

th

e fi

rst

colu

mn

?

•F

or t

hos

e st

atem

ents

th

at y

ou m

ark

wit

h a

D,u

se a

pie

ce o

f pa

per

to w

rite

an

ex

ampl

e of

wh

y yo

u d

isag

ree.

11

Answers (Anticipation Guide and Lesson 11-1)

Chapter 11 A1 Glencoe California Mathematics, Grade 6

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Skill

s Pr

actic

eA

rea

of

Par

alle

log

ram

s

Cha

pter

11

11G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–1

pygp

11-1

Fin

d t

he

area

of

each

par

alle

logr

am.R

oun

d t

o th

e n

eare

st t

enth

if

nec

essa

ry.

1.ba

se �

5 ft

2.ba

se �

9 in

.h

eigh

t �

12 f

t60

ft2

hei

ght

�2

in.

18 in

2

3.ba

se �

6 cm

4.ba

se �

4 �2 5�

yd

hei

ght

�5.

5 cm

33 c

m2

hei

ght

�2

yd8 �

4 5�yd

2

5.ba

se �

15.3

mm

6.ba

se �

19.6

mh

eigh

t �

8 m

m12

2.4

mm

2h

eigh

t �

14.5

m28

4.2

m2

7.6

cm2

8.28

in2

9.16

5 m

m2

10.

108

ft2

11.

4.6

cm2

12.

236

in2

13.

51.6

mm

214

.50

4 ft

2o

r 56

yd

2

7 yd

24 ft

4.3

mm

12 m

m

20 in

. 11

in.

4 5

2.3

cm

2 cm

12 ft

9 ft

15 m

m

11 m

m

7 in

.

4 in

.

2 cm

3 cm

6AF

3.1,

6A

F3.

2

Exam

ple

1

Exam

ple

2

Exer

cise

s

Fin

d t

he

area

of

a p

aral

lelo

gram

if

the

bas

e

is 6

in

ches

an

d t

he

hei

ght

is 3

.7 i

nch

es.

Est

imat

eA

�6

�4

or 2

4 in

2

A�

bhA

rea

of a

par

alle

logr

am

A�

6�

3.7

Rep

lace

b w

ith 6

and

hw

ith 3

.7.

A�

22.2

Mul

tiply

.

Th

e ar

ea o

f th

e pa

rall

elog

ram

is

22.2

squ

are

inch

es.T

his

is c

lose

to

the

estim

ate.

Fin

d t

he

area

of

the

par

alle

logr

am a

t th

e ri

ght.

Est

imat

eA

�10

�10

or

100

cm2

A�

bhA

rea

of a

par

alle

logr

am

A�

12 �

8R

epla

ce b

with

12

and

hw

ith 8

.

A�

96M

ultip

ly.

Th

e ar

ea o

f th

e pa

rall

elog

ram

is

96 s

quar

e ce

nti

met

ers.

Thi

s is

clo

se t

o th

e es

timat

e.

Fin

d t

he

area

of

each

par

alle

logr

am.R

oun

d t

o th

e n

eare

st t

enth

if

nec

essa

ry.

1.2.

3.

66 f

t236

.8 m

m2

272

in2

17 in

.

16 in

.

4.6

mm

8 m

m

5 ft

13.2

ft

12 c

m

8 cm3.

7 in

.

6 in

.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Are

a o

f P

aral

lelo

gra

ms

Cha

pter

11

10G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

11-1

The

are

a A

of a

par

alle

logr

am e

qual

s th

e pr

oduc

t of

its

base

ban

d its

hei

ght

h.

A�

bh

The

base

is a

ny s

ide

of a

par

alle

logr

am.

The

heig

ht is

the

leng

th o

fth

e se

gmen

t per

pend

icul

arto

the

base

with

end

poin

tson

opp

osite

sid

es.

b

h

6AF

3.1,

6A

F3.

2

Answers (Lesson 11-1)


An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Are

a o

f P

aral

lelo

gra

ms

Cha

pter

11

13G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–1

pygp

11-1

1.SA

ILS

Joyc

e w

ants

to

con

stru

ct a

sai

lw

ith

th

e di

men

sion

s sh

own

.How

mu

chm

ater

ial

wil

l be

use

d?35

0 ft

2

14 ft25

ft

2.SI

GN

SP

edro

wan

ts t

o m

ake

the

sign

in

the

shap

e sh

own

an

d n

eeds

to

know

how

mu

ch m

ater

ial

wil

l be

nee

ded.

Wh

at i

s th

e ar

ea o

f th

e si

gn?

1,05

0 in

2 30 in

.

35 in

.

Yard

Sale

3.SH

AD

ING

Alm

a’s

engi

nee

rin

g fi

rm m

ust

dete

rmin

e th

e ar

ea o

f th

e la

rges

tn

oon

tim

e sh

adow

th

at a

pro

pose

dbu

ildi

ng

desi

gn w

ill

crea

te.W

hat

is

the

area

of

the

shad

ow?

2,24

0 ft

2

40 ft

56 ft

4.PO

OLS

Tam

ika

has

des

ign

ed a

poo

l in

the

shap

e sh

own

.Wh

at i

s th

e ar

ea o

fth

e bo

ttom

of

the

pool

if

the

surf

ace

ispe

rfec

tly

flat

?60

0 m

2

30 m

20 m

5.C

ITY

PLA

NN

ING

Tw

o pa

rall

el s

tree

ts a

recu

t ac

ross

by

two

oth

er p

aral

lel

stre

ets

as s

how

n i

n t

he

figu

re,c

utt

ing

off

apa

rcel

of

lan

d in

th

e sh

ape

of a

para

llel

ogra

m.F

ind

the

area

of

the

parc

el o

f la

nd.

85,0

00 f

t2

250

ft

340

ft

Mai

n St

reet

Dres

den

Way

Columbus Ave.

Jefferson Ave.

6.TA

RPS

Nek

a w

ants

to

cut

a ta

rp i

n t

he

shap

e sh

own

.Wh

at i

s th

e m

inim

um

amou

nt

of c

anva

s cl

oth

th

at h

e w

ill

nee

d?1,

440

ft2

36 ft

40 ft

6AF

3.1,

6A

F3.

2

Fin

d t

he

area

of

each

par

alle

logr

am.R

oun

d t

o th

e n

eare

st t

enth

if

nec

essa

ry.

1.2.

3.

36.9

mm

214

4 m

25.

2 yd

2

4.5.

6.

60 in

20.

63 c

m2

182

ft2

7.8.

9.

162

ft2

or

18 y

d2

360

in2

or

2.5

ft2

1,29

6 in

2o

r 9

ft2

or

1 yd

2

GEO

GR

APH

YE

stim

ate

the

area

of

each

sta

te.

10.

55,9

00 m

i211

.7,

425

mi2

12.

ALG

EBR

AA

par

alle

logr

am h

as a

n a

rea

of24

0 sq

uar

e m

eter

s.F

ind

the

hei

ght

of t

he

para

llel

ogra

m i

f th

e ba

se i

s 20

met

ers.

12 m

13.

ALG

EBR

AW

hat

is

the

base

of

a pa

rall

elog

ram

if t

he

hei

ght

is 5

fee

t an

d th

e ar

ea i

s 65

squ

are

feet

?13

ft

5 ft

b ft

A �

65

ft2

20

m h m

A �

240

m2

55

mi

135

mi

New

Jers

ey

260

mi

215

mi

Iow

a

1.5

yd

24 in

.

2 ft

15

in.

18

ft

3 y

d

13

ft 1

4 ft

15

ft

1 4

0.9

cm

0.7

cm

0.8

cm

11

in.

8 in

.

7

in.

1 2

5.2

yd

1 y

d

12

m

12

m

4.5

mm

8.2

mm

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Are

a o

f P

aral

lelo

gra

ms

Cha

pter

11

12G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


11-1

6AF

3.1,

6A

F3.

2



Exer

cise

s

Exam

ple

2

Exam

ple

1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Spre

adsh

eet A

ctiv

ityA

reas

of

Par

alle

log

ram

s

Cha

pter

11

15G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–1

pygp

11-1

You

can

use

a s

prea

dshe

et t

o de

term

ine

the

area

of

a pa

ralle

logr

am.

Use

a s

prea

dshe

et t

o fi

nd t

he a

rea

of a

par

alle

logr

am w

ith

base

equ

al t

o 5

inch

es a

nd h

eigh

t eq

ual t

o 4

inch

es.

Step

1U

se c

ell A

1of

the

spre

adsh

eet f

or th

e ba

se o

f th

e pa

rall

elog

ram

and

cel

l B1

for

the

heig

htof

the

para

llel

ogra

m.

Step

2In

cel

l C1,

ent

er a

n eq

uals

sig

n fo

llow

ed b

y th

e fo

rmul

a fo

r th

e ar

ea o

f a

para

llel

ogra

m.

The

for

mul

a sh

ould

be

�A1

*B1.

The

n pr

ess

ENTE

Rto

ret

urn

the

area

.

The

are

a of

the

para

llel

ogra

m is

20

squa

re in

ches

.

Use

a s

prea

dshe

et t

o fi

nd t

he a

rea

of a

para

llelo

gram

wit

h ba

se e

qual

to

2.5

cent

imet

ers

and

heig

ht e

qual

to

3.5

cent

imet

ers.

Step

3E

nter

the

base

in c

ell A

2an

dth

e he

ight

in c

ell B

2.

Step

4C

lick

on

the

bott

om r

ight

cor

ner

of c

ell C

1an

d dr

ag it

to C

2. T

his

retu

rns

the

area

of

the

para

llel

ogra

m.

The

are

a of

the

para

llel

ogra

m is

8.7

5 sq

uare

cen

tim

eter

s.

Use

a s

pre

adsh

eet

to f

ind

th

e ar

eas

of t

he

give

n p

aral

lelo

gram

s.

1.b

�3

in.,

h�

6 in

.2.

b�

2 in

., h

�5

in.

3.b

�5

in.,

h�

1 in

.18

in2

10 in

25

in2

4.b

�7

in.,

h�

3 in

.5.

b�

3.5

m, h

�1.

5 m

6.b

�2.

2 m

, h�

1.7

m21

in2

5.25

m2

3.74

m2

7.b

�1.

5 m

, h�

0.1

m8.

b�

5.7

m, h

�9.

1 m

9.b

�0.

5 m

, h�

0.3

m0.

15 m

251

.87

m2

0.15

m2

AB

DC

1 2 3 4S

hee

t 1

52.

520

2.5

3.5

8.75

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

11

14G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


11-1

Two

Are

a Pu

zzle

sC

ut

out

the

five

pu

zzle

pie

ces

at t

he

bot

tom

of

this

pag

e.T

hen

use

them

to

solv

e th

ese

two

pu

zzle

s.

1.U

se a

ll f

ive

puzz

le p

iece

s to

mak

e2.

Use

th

e fo

ur

larg

est

piec

es t

o m

ake

a sq

uar

e w

ith

an

are

a of

9 s

quar

ea

squ

are

wit

h a

n a

rea

of 8

squ

are

inch

es.R

ecor

d yo

ur

solu

tion

bel

ow.

inch

es.R

ecor

d yo

ur

solu

tion

bel

ow.

2 in

.

1 in

.

1 in

.

2 in

.

2 in

.

1 in

2

6AF

3.1,

6A

F3.

2



An

swer

s

Exer

cise

s

Exam

ple

2

Exam

ple

1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

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ut

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,th

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ple

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swer

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e b

ase

can

be

any

sid

e o

f th

e tr

ian

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.

6.H

ow d

o yo

u f

ind

the

hei

ght

of a

tri

angl

e?S

amp

le a

nsw

er:

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ceyo

u k

no

w w

hic

h s

ide

is t

he

bas

e,fi

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igh

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nd

outs

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he

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se t

rian

gle

8.H

ow i

s th

e h

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t of

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rape

zoid

sim

ilar

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angl

e or

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rall

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?S

amp

le a

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er:

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per

pen

dic

ula

r to

th

e b

ase.

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emb

er W

hat

Yo

u L

earn

ed9.

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e M

ini

Lab

in

th

is l

esso

n g

ave

you

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ood

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r th

efo

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ing

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.Th

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o yo

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yth

ing

in t

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form

ula

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ple

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ing

�1 2�(b

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ns

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ind

th

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erag

e o

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ng

ths

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bas

es.S

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len

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ases

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7 ft

11

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ME

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11-2

Fin

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An

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11-3

Get

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p o

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h p

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the

cen

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ris

wh

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th

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eate

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ess

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equ

al t

o

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hat

can

you

say

abo

ut

the

dist

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m G

to H

and

the

dist

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hal

f o

f F

to J

.

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ind

the

dist

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5 ft

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d t

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on

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he

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r �

repr

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and

non

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um

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n?

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ple

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th

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wh

ose

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int

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d o

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sym

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g th

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ple

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e sy

mb

ol �

is u

sed

wh

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nu

mb

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su

bst

itu

ted

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r �

in t

he

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ula

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se a

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mb

er in

pla

ceo

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at n

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nly

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pro

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atio

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circ

um

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als

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nly

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on

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11-3

You

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et to

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valu

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�. Y

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ill n

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r it

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the

circ

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a pi

ece

of s

trin

g.T

hen

use

a m

etri

c ru

ler

to r

ecor

d th

e m

easu

rem

ent i

n m

illi

met

ers.

Als

ore

cord

the

mea

sure

of

the

diam

eter

of

each

obj

ect i

n m

illi

met

ers.

Cre

ate

a sp

read

shee

t wit

h th

ree

colu

mns

. In

colu

mn

A, e

nter

the

circ

umfe

renc

es o

f th

e it

ems

you

mea

sure

d. I

n co

lum

n B

, ent

er th

edi

amet

ers.

In

colu

mn

C, c

reat

e a

form

ula

for

the

valu

e of

�us

ing

circ

umfe

renc

e an

d di

amet

er. L

et th

e sp

read

shee

t cal

cula

te th

e va

lue

for

asm

any

deci

mal

pla

ces

as it

can

.

You

r sp

read

shee

t sho

uld

look

like

this

.

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you

r sp

read

shee

t to

an

swer

th

e fo

llow

ing

qu

esti

ons.

1.W

hat i

s th

e va

lue

of �

used

by

your

spr

eads

heet

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amp

le a

nsw

er:3

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5926

54

2.H

ow c

lose

are

you

r ca

lcul

atio

ns to

the

actu

al v

alue

of

�?

To h

ow

man

y de

cim

al p

lace

s ar

e yo

ur c

alcu

lati

ons

corr

ect?

An

swer

s w

ill v

ary.

3.W

hat c

ause

s yo

ur c

alcu

lati

ons

of �

not t

o be

exa

ct?

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ple

an

swer

:Mea

sure

men

tsm

ade

wit

h a

str

ing

are

inac

cura

te.I

t is

har

d t

o f

ind

th

e ex

act

dia

met

eru

nle

ss t

he

cen

ter

is la

bel

ed. S

amp

le

4.W

hat c

ould

mak

e yo

ur c

alcu

lati

ons

mor

e ex

act?

Sam

ple

an

swer

:Use

sci

enti

fic

inst

rum

ents

to

get

mo

re e

xact

mea

sure

men

ts

5.S

uppo

se y

ou c

reat

ed a

noth

er s

prea

dshe

et w

ith

the

sam

e co

lum

ns a

s th

is o

ne. T

he n

ew s

prea

dshe

et c

alcu

late

s th

e di

amet

er w

hen

give

n th

e ci

rcum

fere

nce

and

the

valu

e of

�. W

hat f

orm

ula

wou

ld y

ou e

nter

in

colu

mn

B?

�A

/C

6.If

you

cre

ate

anot

her

spre

adsh

eet t

hat c

alcu

late

s th

e ci

rcum

fere

nce

whe

n gi

ven

the

diam

eter

and

the

valu

e of

�, w

hat f

orm

ula

wou

ld y

ou e

nter

in

colu

mn

A?

�C

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AB

DC

1 2 3S

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t 1

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cise

s

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ple

2

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ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

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IOD

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ide

and

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y 78

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at h

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y 69

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d t

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cle.

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r �

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nd

to

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nea

rest

ten

th.

1.2.

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us

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ple

1

6MG

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NA

ME

____

____

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____

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IOD

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on

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te t

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i L

ab a

t th

e to

p o

f p

age

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in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

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1.W

hat

is

the

mea

sure

men

t of

th

e ba

se a

nd

the

hei

ght?

�1 2�C;

r

2.S

ubs

titu

te t

hes

e va

lues

in

to t

he

form

ula

for

th

e ar

ea o

f a

para

llel

ogra

m.

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3.R

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wit

h t

he

expr

essi

on f

or t

he

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um

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nce

of

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rcle

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impl

ify

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atio

n a

nd

desc

ribe

wh

at i

t re

pres

ents

.

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r)(r

);A

��

r2;

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area

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rcle

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d t

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on

4.T

he

form

ula

for

th

e ar

ea o

f a

circ

le u

ses

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nu

mbe

r �

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doe

s th

isaf

fect

th

e va

lue

of t

he

area

of

a ci

rcle

fou

nd

usi

ng

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form

ula

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amp

le a

nsw

er:W

hen

yo

u s

ub

stit

ute

a v

alu

e fo

r �

or

use

a

calc

ula

tor

to m

ult

iply

by

�,t

he

resu

lt w

ill b

e o

nly

an

esti

mat

e.

5.If

you

are

giv

en t

he

len

gth

of

the

diam

eter

of

a ci

rcle

,how

can

you

fin

d it

sar

ea?

Sam

ple

an

swer

:D

ivid

e th

e le

ng

th o

f th

e d

iam

eter

by

2,sq

uar

e it

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d m

ult

iply

th

e re

sult

by

pi.

Rem

emb

er W

hat

Yo

u L

earn

ed6.

Th

ink

abou

t th

e fo

rmu

las

you

hav

e le

arn

ed t

hat

in

volv

e ci

rcle

s:C

�2�

ror

C�

�d

and

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hel

p yo

u r

emem

ber

the

diff

eren

ce b

etw

een

th

efo

rmu

las

for

circ

um

fere

nce

an

d th

e fo

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rea,

thin

k ab

out

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eren

ces

in t

he

un

its

use

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r ea

ch m

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rem

ent.

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its

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use

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r ea

ch?

How

can

th

is h

elp

you

rem

embe

r th

e fo

rmu

la f

or t

he

area

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rcle

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amp

le a

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er:T

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e sa

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r th

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th

at m

igh

t h

elp

yo

ure

mem

ber

th

at t

he

form

ula

fo

r th

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f a

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pi t

imes

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its

rad

ius.

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r π.

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nd

to

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nea

rest

ten

th i

f n

eces

sary

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imat

e to

fin

d t

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roxi

mat

e ar

ea o

f ea

ch c

ircl

e.

13.

14.

15.

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ple

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swer

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amp

le a

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ple

an

swer

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23

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SPO

TLIG

HT

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t ca

n b

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ed t

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fect

ivel

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ght

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lar

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p to

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eter

s in

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met

er.T

o th

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eare

st t

enth

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at i

s th

e m

axim

um

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e ef

fect

ivel

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t by

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AR

CH

ERY

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ll’s

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y ta

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re t

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t h

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ches

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d th

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NA

ME

____

____

____

____

____

____

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____

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____

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ER

IOD

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Prac

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o yo

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ME

____

____

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____

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ER

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ract

ice

Are

a o

f C

ircl

es

Cha

pter

11

34G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


11-4

1.PO

OLS

Su

san

des

ign

ed a

cir

cula

r po

olw

ith

a d

iam

eter

of

25 m

eter

s.W

hat

is

the

area

of

the

bott

om o

f th

e po

ol?

Rou

nd

to t

he

nea

rest

ten

th.

490.

6 m

2

2.M

ON

EYF

ind

the

area

of

the

coin

to

the

nea

rest

ten

th.

283.

4 m

m2

19 m

m

3.D

RU

MS

Wh

at i

s th

e ar

ea o

f th

edr

um

hea

d on

th

e dr

um

sh

own

bel

ow?

Rou

nd

to t

he

nea

rest

ten

th.

153.

9 in

214 in

.

4.PI

ZZA

Est

imat

e th

e ar

ea o

f th

e to

p of

aro

un

d pi

zza

that

has

a d

iam

eter

of

16 i

nch

es.R

oun

d to

th

e n

eare

st t

enth

.20

1.0

in2

5.G

AR

DEN

ING

Jan

e n

eeds

to

buy

mu

lch

for

the

gard

en w

ith

th

e di

men

sion

ssh

own

in

th

e fi

gure

.For

how

mu

ch a

rea

does

Jan

e n

eed

to b

uy

mu

lch

? R

oun

d to

the

nea

rest

ten

th. 95

.0 y

d2

5.5

yd

6.U

TILI

TIES

Wh

at i

s th

e ar

ea o

f th

e to

psu

rfac

e of

a c

ircu

lar

man

hol

e co

ver

that

has

a r

adiu

s of

30

cen

tim

eter

s? U

se3.

14 f

or �

. 2,8

26 c

m2

6MG

1.1,

6M

G1.

2



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

11

37G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–5

pygp

11-5

Sol

ve a

sim

ple

r p

rob

lem

to

solv

e.

1.PO

OL

Fin

d th

e ar

ea o

f th

e si

dew

alk

arou

nd

the

pool

sh

own

bel

ow.

376

ft2

2.G

EOM

ETRY

Fin

d th

e ar

ea o

f th

e sh

ape

show

n.

34 c

m2

3.PO

PULA

TIO

NT

he

popu

lati

on o

f G

hos

tow

n,U

SA

is

decr

easi

ng

at a

rat

e of

3 pe

ople

per

yea

r.If

th

ere

are

curr

entl

y 83

1 pe

ople

liv

ing

in t

he

tow

n,

wh

en w

ill

the

tow

n b

e de

sert

ed?

277

year

s

4.ST

AIN

ED G

LASS

Fin

d th

e ar

ea o

f th

e st

ain

ed g

lass

win

dow

sh

own

bel

ow.

Use

3.1

4 fo

r π.

Rou

nd

to t

he

nea

rest

hu

ndr

edth

if

nec

essa

ry.

6.58

in2

5.ST

OV

ETO

PSW

hat

is

the

area

of

the

stov

etop

sh

own

,not

in

clu

din

g th

ebu

rner

s? U

se 3

.14

for

π.R

oun

d to

th

e n

eare

st h

un

dred

th i

f n

eces

sary

.

4.23

ft2

6.PO

OLS

Wat

er i

s be

ing

adde

d at

a r

ate

of 5

0 ga

llon

s pe

r m

inu

te t

o a

pool

.H

ow l

ong

wil

l it

tak

e u

nti

l th

e 10

,000

gal

lon

poo

l is

fu

ll?

200

min

ute

s o

r 3

ho

urs

an

d 2

0 m

inu

tes

3 ft

0.7

5 ft

2 ft

1.6

in.

1.6

in.

3 c

m

8 c

m

8 c

m

2 c

m

2 ft

60

ft 3

0 ft

2 ft

6MR

1.3,

6M

R2.

2, 6

NS

2.1

Skill

s Pr

actic

eP

rob

lem

-So

lvin

g In

vest

igat

ion

:S

olv

e a

Sim

ple

r P

rob

lem

Exer

cise

s

SPO

RTS

Wes

t H

igh

Sch

ool

wan

ts t

op

ain

t fi

eld

blu

e,b

ut

not

th

e ce

nte

r.T

he

dia

gram

bel

ow s

how

s th

e d

imen

sion

s of

the

fiel

d a

nd

cen

ter

circ

le.H

ow m

uch

area

wil

l th

ey n

eed

to

pai

nt

blu

e?

1.FR

AM

ESJo

an w

ants

to

pain

t h

er f

avor

ite

pict

ure

fr

ame.

How

mu

ch p

ain

t w

ould

sh

e n

eed

to u

se i

nor

der

to c

over

just

th

e fr

ame?

41 in

2

2.W

ALL

PAPE

RR

ich

ard

wan

ts t

o w

allp

aper

on

e w

all

of h

is b

ath

room

.He

has

tw

o se

mi-

circ

ula

r w

indo

ws

alon

g th

e w

all.

How

mu

ch w

allp

aper

m

ust

he

purc

has

e?83

.44

ft2

12

ft

8 ft

2 ft

2 ft

10

in.

10

in.

3 in

.

3 in

. 100

ft

75 ft

30

ft

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

11

36G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


11-5

Wh

en p

robl

em s

olvi

ng,

som

etim

es i

t is

eas

ier

to s

olve

a s

imp

ler

pro

ble

mfi

rst

to f

ind

the

corr

ect

stra

tegy

for

sol

vin

g a

mor

e di

ffic

ult

pro

blem

.

Exp

lore

You

kn

ow t

hat

th

e fi

eld

is o

ne

larg

e re

ctan

gle

and

the

cen

ter

sym

bol

is a

larg

e ci

rcle

.

Pla

nYo

u c

an f

ind

the

area

of

the

rect

angl

e an

d th

e ar

ea o

f th

e ci

rcle

an

dsu

btra

ct.

Sol

veA

rea

of r

ecta

ngl

e:A

��

wA

�10

0�

75 o

r 75

00

Are

a if

cir

cle:

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�r2

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3.14

�15

2or

706

.5

Su

btra

ct:

7500

�70

6.5

or 6

793.

5 ft

2

So,

they

wou

ld n

eed

to p

ain

t 6,

793.

5 sq

uar

e fe

et o

f fi

eld.

Ch

eck

Use

est

imat

ion

to

chec

k.T

he

area

of

the

enti

re f

ield

is

7,50

0 ft

an

d th

eci

rcle

is

appr

oxim

atel

y 70

0 fe

et s

o th

e ar

ea s

hou

ld b

e le

ss t

han

6,8

00 f

eet.

Sin

ce 6

,793

.5 i

s le

ss t

han

6,8

00 f

t,th

e an

swer

is

reas

onab

le.

Exam

ple

6MR

1.3,

6M

R2.

2, 6

NS

2.1

Stud

y Gu

ide

and

Inte

rven

tion

Pro

ble

m-S

olv

ing

Inve

stig

atio

n:

So

lve

a S

imp

ler

Pro

ble

m



Sol

ve e

ach

pro

ble

m u

sin

g an

y st

rate

gy y

ou h

ave

lear

ned

.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

11

39G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–5

pygp

11-5

1.A

REA

Fin

d th

e ar

ea o

f th

e fi

gure

bel

ow.

Use

3.1

4 fo

r π.

44.5

6 in

2

8 in

.

4 in

.

2.M

ON

EYT

he

tabl

e be

low

sh

ows

the

amou

nt

of m

oney

Sh

osh

i ea

rned

for

wor

kin

g va

riou

s h

ours

.Wri

te a

ru

le t

ore

pres

ent

the

amou

nt

of p

ay,P

,bas

edon

th

e n

um

ber

of h

ours

wor

ked,

h.

P =

5.5

h

3.SA

LES

For

eve

ry n

icke

l in

crea

se i

npr

ice,

the

subs

crip

tion

s to

th

eP

erry

svil

le P

aper

dec

reas

es b

y 5

peop

le.

If 1

,256

peo

ple

curr

entl

y su

bscr

ibe

toth

e P

aper

,how

man

y pe

ople

wil

lsu

bscr

ibe

to i

t if

th

e pr

ice

is i

ncr

ease

dby

$0.

25?

1,23

1 p

eop

le

4.SC

ALE

DR

AW

ING

Sh

ann

on i

s cr

eati

ng

asc

ale

draw

ing

of h

er c

lass

room

.If

she

is

usi

ng

the

scal

e 1

foot

��1 2�

inch

an

d th

e

room

mod

el i

s 10

in

ches

by

15 i

nch

es,

wh

at a

re t

he

dim

ensi

ons

of t

he

actu

alro

om?

20 f

t by

30

ft

5.ST

UD

Y T

IME

Th

e ci

rcle

gra

ph b

elow

show

s th

e re

sult

s to

a s

urv

ey a

skin

gst

ude

nts

how

lon

g th

ey s

tudy

eac

hn

igh

t.In

a s

choo

l of

400

stu

den

ts,h

owm

any

stu

den

ts s

tudy

1.5

– 2

.5 h

ours

per

nig

ht?

260

stu

den

ts3–

4 ho

urs

10%

1.5–

2.5

hour

s65

%

0–1

hour

s65

%

6.PH

OTO

GR

APH

YW

hat

is

the

area

of

the

mat

te p

ictu

red

belo

w?

39 in

2

1.5

in.

4 in

.

6 in

.

1.5

in.

7.TR

AV

ELH

ow f

ar h

as K

im t

rave

led

ifsh

e h

as d

rive

n 4

5 m

iles

per

hou

r fo

r 4

hou

rs?

180

mile

s

8.SI

STER

SA

nge

la i

s 3

year

s ol

der

than

Su

sie.

Bec

ca i

s 2

year

s yo

un

ger

than

Su

sie.

If B

ecca

is

10 y

ears

old

,how

old

are

Su

sie

and

An

gela

?12

an

d 1

5

Hou

rs1

23

Pay

5.50

11.0

016

.50

6MR

1.3,

6M

R2.

2, 6

NS

2.1

Wor

d Pr

oble

m P

ract

ice

Pro

ble

m-S

olv

ing

Inve

stig

atio

n:

So

lve

a S

imp

ler

Pro

ble

m

Sele

ct t

he

Op

erat

ion

Mix

ed P

rob

lem

Sol

vin

g

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

11

38G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


11-5

Sol

ve E

xerc

ises

1 a

nd

2.U

se t

he

solv

e a

sim

ple

r p

rob

lem

str

ateg

y.

1.ST

AD

IUM

Th

e ex

its

in a

sta

diu

m a

rede

sign

ed t

o al

low

1,2

00 p

eopl

e to

lea

veth

e st

adiu

m e

ach

min

ute

.At

this

rat

e,h

ow l

ong

wou

ld i

t ta

ke f

or 1

0,80

0 pe

ople

to l

eave

th

e st

adiu

m?

9 m

inu

tes

2.PH

AR

MA

CY

A c

ity

has

th

ree

maj

orph

arm

acy

chai

ns

wh

ich

hav

e a

tota

l of

895,

000

cust

omer

s.A

ppro

xim

atel

y h

owm

any

cust

omer

s do

bu

sin

ess

at e

ach

maj

or p

har

mac

y?

Sam

ple

an

swer

:0.

55�

900,

000

or

495,

000

cust

om

ers

use

ph

arm

acy

A;

0.32

�90

0,00

0 o

r 28

8,00

0 cu

sto

mer

su

se p

har

mac

y B

;0.

13 �

900,

000

or

117,

000

cust

om

ers

use

ph

arm

acy

CU

se a

ny

stra

tegy

to

solv

e E

xerc

ises

3an

d 4

.Som

e st

rate

gies

are

sh

own

bel

ow.

3.C

AR

PEN

TRY

Mr.

Fer

nan

dez

use

s 7

boar

ds t

hat

are

4 f

eet

lon

g an

d 6

inch

esw

ide

to m

ake

one

book

shel

f.If

he

buys

lum

ber

in l

engt

hs

of 8

fee

t w

ith

a w

idth

of 1

2 in

ches

,how

man

y pi

eces

of

lum

ber

does

he

nee

d to

pu

rch

ase

to m

ake

5bo

oksh

elve

s?

9 p

iece

s

4.A

REA

Sta

cey

is m

akin

g a

stai

ned

gla

ssw

indo

w a

bove

her

fro

nt

door

way

in

th

esh

ape

as s

how

n i

n t

he

figu

re.T

o th

en

eare

st t

enth

,wh

at i

s th

e ar

ea o

f th

esh

aded

por

tion

of

the

win

dow

?2.

7 ft

2

For

Exe

rcis

es 5

an

d 6

,sel

ect

the

app

rop

riat

e op

erat

ion

(s)

to s

olve

th

ep

rob

lem

s.J

ust

ify

you

r se

lect

ion

(s)

and

solv

e th

e p

rob

lem

.

5.Q

UA

LITY

CO

NTR

OL

For

eve

ry 2

50te

levi

sion

s te

sted

,3 t

elev

isio

ns

are

fou

nd

to b

e de

fect

ive.

How

man

yte

levi

sion

s w

ere

test

ed i

f 48

tel

evis

ion

sw

ere

fou

nd

defe

ctiv

e?

Div

isio

n a

nd

mu

ltip

licat

ion

;48

�3

�16

;16

�25

0�

4,00

0;4,

000

tele

visi

on

s

6.A

PPLI

AN

CE

REP

AIR

An

app

lian

ce r

epai

rco

mpa

ny

char

ged

$35

to m

ake

a h

ouse

call

.Aft

er a

rriv

ing,

the

com

pan

ych

arge

d $1

0 fo

r ev

ery

15 m

inu

tes

ofla

bor.

How

mu

ch w

as t

he

repa

ir b

ill

ifth

e n

ew p

arts

cos

t $2

3 an

d th

eap

plia

nce

too

k 45

min

ute

s to

rep

air?

Mu

ltip

licat

ion

an

d a

dd

itio

n;

3�

10�

30;

35�

23�

30�

88;

$88

3 ft

1 ft

Ph

arm

acy

Per

cen

tA

54.8

%B

32.4

%C

12.8

%

PR

OB

LE

M-S

OL

VIN

G S

TR

AT

EG

IES

•U

se t

he

fou

r-st

ep p

lan

.•

Eli

min

ate

poss

ibil

itie

s.•

Dra

w a

dia

gram

.•

Sol

ve a

sim

pler

pro

blem

.

6MR

1.3,

6M

R2.

2, 6

NS

2.1

Prac

tice

Pro

ble

m-S

olv

ing

Inve

stig

atio

n:

So

lve

a S

imp

ler

Pro

ble

m



An

swer

s

Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Are

a o

f C

om

ple

x F

igu

res

Cha

pter

11

41G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–6

pygp

11-6

Fin

d t

he

area

of

the

figu

re a

t th

e ri

ght

in s

qu

are

feet

.

Th

e fi

gure

can

be

sepa

rate

d in

to a

rec

tan

gle

and

a tr

apez

oid.

Fin

d th

e ar

ea o

f ea

ch.

Are

a of

Rec

tan

gle

A�

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rea

of a

rec

tang

le

A�

12�

8R

epla

ce �

with

12

and

ww

ith 8

.

A�

96M

ultip

ly.

Are

a of

Tra

pezo

id

A�

�1 2�h(b

1�

b 2)

Are

a of

a t

rape

zoid

A�

�1 2�(4)

(4�

12)

Rep

lace

hw

ith 4

, b 1

with

4,

and

b 2w

ith 1

2.

A�

32M

ultip

ly.

Th

e ar

ea o

f th

e fi

gure

is

96 �

32 o

r 12

8 sq

uar

e fe

et.

Fin

d t

he

area

of

each

fig

ure

.Use

3.1

4 fo

r �

.Rou

nd

to

the

nea

rest

ten

th i

f n

eces

sary

.

1.65

cm

22.

25.4

in2

3.80

6.0

mm

218

mm 38

mm

11 m

m

4 in

.5

in.

4 cm

6.5

cm

13 c

m

6 cm

6 cm

12 ft

4 ft

4 ft

12 ft

8 ft

12 ft

4 ft

4 ft

8 ft

Co

mp

lex

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ure

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iang

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qua

drila

tera

ls, s

emic

ircle

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ther

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dim

ensi

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the

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Get

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ple

an

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ind

th

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ea o

f ea

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oo

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Less

on

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term

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1.H

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o yo

u k

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ind

th

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ng

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emb

er W

hat

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in a

dic

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ary

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wh

en u

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an a

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th

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esso

n.

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n t

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1 a

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side

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s?S

amp

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11-6

Fin

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area

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area

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any

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you

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fin

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rea?

256

ft2 ;

Sam

ple

an

swer

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5.W

hat

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the

area

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the

den

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hat

wou

ld t

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area

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den

be

if t

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sem

icir

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r w

indo

w w

ere

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oved

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plac

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lat

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hat

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the

area

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rec

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r co

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feet

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any

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ill

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352

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328

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6AF

3.1,

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F3.

2



Exer

cise

s

For

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obj

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real

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aces

of

a pr

ism

are

___

____

____

____

an

d ar

e

____

____

____

___.

bas

es;

par

alle

l

3.T

he

shap

e of

th

e ba

se t

ells

th

e n

ame

of t

he

____

____

____

___.

pyr

amid

or

pri

sm

4.T

he

base

of

a co

ne

is a

___

____

____

____

.ci

rcle

5.A

___

____

____

____

has

no

face

s,ba

ses,

edge

s,or

ver

tice

s.cy

lind

er

6.T

he

base

s of

a c

ylin

der

are

____

____

____

___.

circ

les

7.A

ll o

f th

e po

ints

on

a _

____

____

____

__ a

re t

he

sam

e di

stan

ce f

rom

th

e

____

____

____

___.

cylin

der

;ce

nte

r o

r ax

is

Rem

emb

er W

hat

Yo

u L

earn

ed8.

Com

pare

an

d co

ntr

ast

a tr

ian

gula

r pr

ism

,a t

rian

gula

r py

ram

id,a

nd

aco

ne.

A t

rian

gu

lar

pri

sm h

as 2

tri

ang

ula

r b

ases

;it

has

th

ree

late

ral

face

s th

at a

re r

ecta

ng

les.

A t

rian

gu

lar

pyr

amid

has

a t

rian

gle

bas

e;it

has

on

e b

ase

and

th

ree

tria

ng

le s

ides

.A

co

ne

has

a c

ircl

e b

ase;

it h

as o

ne

vert

ex a

nd

no

ed

ges

.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Less

on R

eadi

ng G

uide

Th

ree

Dim

ensi

on

al F

igu

res

Cha

pter

11

46G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


11-7

7MG

3.6



An

swer

s

For

eac

h f

igu

re,i

den

tify

th

e sh

ape

of t

he

bas

e(s)

,if

any.

Th

en c

lass

ify

the

figu

re.

1.2.

3.

pen

tag

on

s;ci

rcle

s;cy

lind

ertr

ian

gle

s;p

enta

go

nal

pri

smtr

ian

gu

lar

pri

sm

4.5.

6.

circ

le;

con

eh

exag

on

;re

ctan

gle

;h

exag

on

al p

yram

idre

ctan

gu

lar

pyr

amid

7.8.

9.

no

ne;

sph

ere

rect

ang

les;

trap

ezo

id;

rect

ang

ula

r p

rism

trap

ezo

idal

pyr

amid

10.

CA

ND

LES

Wh

at t

hre

e-di

men

sion

al

figu

re d

escr

ibes

th

e ca

ndl

e sh

own

?cy

lind

er

11.

FEN

CES

Th

e ba

sic

shap

e of

a f

ence

pos

t is

mad

e of

tw

oge

omet

ric

figu

res.

Cla

ssif

y th

ese

figu

res.

rect

ang

ula

r p

rism

an

d

rect

ang

ula

r p

yram

id

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Th

ree-

Dim

ensi

on

al F

igu

res

Cha

pter

11

49G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–7

pygp

11-7

7MG

3.6

For

eac

h f

igu

re,i

den

tify

th

e sh

ape

of t

he

bas

e(s)

.Th

en c

lass

ify

the

figu

re.

1.2.

3.

rect

ang

les;

circ

les;

cylin

der

rect

ang

ula

r p

rism

squ

ares

;cu

be

4.5.

6.

circ

le;

con

en

on

e;sp

her

etr

ian

gle

;

7.8.

9.

squ

are;

circ

le;

cylin

der

circ

le;

con

e

10.

11.

12.

rect

ang

les;

no

ne;

sph

ere

tria

ng

les;

tria

ng

ula

r re

ctan

gu

lar

pri

smp

rism

13.

14.

15.

rect

ang

les;

squ

ares

;cu

be

circ

les;

cylin

der

rect

ang

ula

r p

rism

NA

ME

____

____

____

____

____

____

____

____

____

____

DA

TE

___

____

____

___

PE

RIO

D

____

_

Skill

s Pr

actic

eT

hre

e-D

imen

sio

nal

Fig

ure

s

Cha

pter

11

48G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


11-7

7MG

3.6

tria

ng

ula

r p

yram

id

squ

are

pyr

amid



Pro

per

ties

of

Pris

ms

Leo

nar

d E

ule

r,bo

rn i

n 1

707,

was

on

e of

th

e w

orld

’s g

reat

est

mat

hem

atic

ian

s.O

ne

of h

isac

com

plis

hm

ents

was

dis

cove

rin

g a

form

ula

for

cal

cula

tin

g th

e n

um

ber

of f

aces

,edg

es,a

nd

vert

ices

on

a t

hre

e-di

men

sion

al f

igu

re.H

e fo

un

d th

at V

�F

�E

�2.

(Ver

tice

s�

Face

s�

Edg

es�

2)

A t

rian

gula

r pr

ism

has

6 v

erti

ces,

5 fa

ces,

and

9 ed

ges.

It h

asth

e fe

wes

t fa

ces,

edge

s,an

d ve

rtic

es o

f an

y pr

ism

.

1.C

ompl

ete

the

tabl

e fo

r a

hex

agon

al a

nd

an o

ctag

onal

pri

sm.

2.If

a p

rism

has

14

vert

ices

an

d 21

edg

es,h

ow m

any

face

s do

es i

t h

ave?

Use

Eu

ler’

s fo

rmu

la.

9 fa

ces

3.A

pri

sm h

as 2

0 ve

rtic

es.H

ow m

any

face

s do

es i

t h

ave?

How

man

y ed

ges?

Th

is p

rism

has

12

face

s an

d 3

0 ed

ges

.(It

is a

“d

ecag

on

alp

rism

”;th

e to

p a

nd

bas

e ea

ch h

ave

10 s

ides

.)4.

An

“n

-gon

al”

pris

m h

as t

wo

base

s,ea

ch w

ith

nsi

des.

Use

th

e pa

tter

ns

inth

e ta

ble

to w

rite

exp

ress

ion

s to

fin

d th

e n

um

ber

of f

aces

,edg

es,a

nd

vert

ices

an

d n

-gon

al p

rism

has

.A

n “

n-g

on

al”

pri

sm h

as n

�2

face

s,3n

edg

es,a

nd

2n

vert

ices

.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enric

hmen

t

Cha

pter

11

51G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–7

pygp

11-7

Pri

smV

erti

ces

Fac

esE

dge

s

tria

ngu

lar

65

9

rect

angu

lar

86

12

pen

tago

nal

107

15

hex

agon

al12

818

octa

gon

al16

1024

7MG

3.6

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Th

ree-

Dim

ensi

on

al F

igu

res

Cha

pter

11

50G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


11-7

1.SP

OR

TSA

reg

ula

tion

bas

ketb

all

wei

ghs

20-2

2 ou

nce

s.C

lass

ify

the

shap

e of

are

gula

tion

bas

ketb

all

as a

th

ree-

dim

ensi

onal

fig

ure

.sp

her

e

2.IC

E C

REA

MT

he

pict

ure

sh

ows

an i

cecr

eam

con

e w

ith

a s

ingl

e sc

oop

on t

op.

Wh

at t

wo

thre

e-di

men

sion

al s

hap

esm

ake

up

the

ice

crea

m a

nd

con

e?

sph

ere

and

co

ne

3.SH

IPPI

NG

Jess

ie b

ough

t a

box

to s

hip

her

gif

ts t

o h

er g

ran

dmot

her

.Cla

ssif

yth

e sh

ape

of a

box

as

a th

ree-

dim

ensi

onal

fig

ure

.re

ctan

gu

lar

pri

sm

4.LA

UN

DRY

Cla

ssif

y th

e sh

ape

of a

th

e la

un

dry

ham

per

show

n a

s a

thre

e-di

men

sion

al f

igu

re.

cylin

der

5.SC

HO

OL

PRO

JEC

TJa

rnel

is

crea

tin

g a

dior

ama

for

his

cla

ss p

roje

ct.H

e pl

ans

to u

se a

sh

oebo

x to

bu

ild

the

dior

ama.

Cla

ssif

y th

e sh

ape

of a

sh

oebo

x as

ath

ree-

dim

ensi

onal

fig

ure

.re

ctan

gu

lar

pri

sm

6.SO

UP

Cla

ssif

y th

e sh

ape

of a

sou

p ca

nas

a t

hre

e-di

men

sion

al f

igu

re.

cylin

der

7.B

AB

Y B

LOC

KS

Cla

ssif

y th

e sh

ape

of t

he

baby

blo

ck a

s a

thre

e-di

men

sion

alfi

gure

.cu

be

8.EA

RTH

Cla

ssif

y th

e sh

ape

of t

he

Ear

thas

a t

hre

e-di

men

sion

al f

igu

re.

sph

ere

7MG

3.6



An

swer

s

Exam

ple

1

Exam

ple

2

Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

11

53G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–8

pygp

11-8

Dra

w a

top

,a s

ide,

and

a f

ron

t vi

ew o

f th

e so

lid

at

the

righ

t.

Th

e to

p vi

ew i

s a

tria

ngl

e.T

he

side

an

d fr

ont

view

s ar

e re

ctan

gles

.

top

side

fron

t

Dra

w t

he

soli

d u

sin

g th

e to

p,s

ide,

and

fro

nt

view

s sh

own

bel

ow.

top

side

fron

t

Step

1U

se t

he

top

view

to

draw

th

e ba

se o

f th

e fi

gure

,a 1

-by-

3 re

ctan

gle.

Step

2A

dd e

dges

to

mak

e th

e ba

se a

so

lid

figu

re.

Step

3U

se t

he

side

an

d fr

ont

view

s to

co

mpl

ete

the

figu

re.

1.D

raw

a t

op,a

sid

e,an

d fr

ont

view

of

the

soli

d.

Sam

ple

an

swer

:

2.D

raw

th

e so

lid

wh

ose

top,

side

,an

d fr

ont

view

s ar

e sh

own

.Use

iso

met

ric

dot

pape

r.

Sam

ple

an

swer

:to

psid

efro

nt

top

side

front

side

fron

t

topfro

nt

top

side

A s

olid

is a

thr

ee-d

imen

sion

al f

igur

e.

5MG

2.3,

6M

R2.

4St

udy

Guid

e an

d In

terv

entio

nD

raw

ing

Th

ree-

Dim

ensi

on

al F

igu

res

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Less

on R

eadi

ng G

uide

Dra

win

g T

hre

e-D

imen

sio

nal

Fig

ure

s

Cha

pter

11

52G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


11-8

Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n a

t th

e to

p o

f p

age

608

in y

our

text

boo

k.

Wri

te y

our

answ

ers

bel

ow.

1.W

hic

h v

iew

of

the

Was

hin

gton

mon

um

ent

is s

how

n i

n t

he

com

ic?

top

2.F

ind

a ph

otog

raph

of

the

Was

hin

gton

Mon

um

ent

and

draw

a s

ide

view

.S

amp

le a

nsw

er:

Rea

d t

he

Less

on

3.A

tw

o-di

men

sion

al f

igu

re h

as t

wo

dim

ensi

ons.

Wh

at a

re t

hey

?le

ng

th a

nd

wid

th

4.A

th

ree-

dim

ensi

onal

fig

ure

has

th

ree

dim

ensi

ons.

Wh

at a

re t

hey

?le

ng

th,w

idth

,an

d d

epth

5.L

abel

th

e di

men

sion

s of

eac

h f

igu

re.

6.U

nde

rlin

e th

e w

ord

that

mak

es t

he

sen

ten

ce t

rue.

A (

rect

angl

e,cu

be)

is a

th

ree-

dim

ensi

onal

fig

ure

.

Rem

emb

er W

hat

Yo

u L

earn

ed7.

Mak

e m

odel

s of

a t

wo-

dim

ensi

onal

fig

ure

an

d a

thre

e-di

men

sion

al f

igu

re.

Use

an

y m

ater

ial

you

lik

e—fo

r ex

ampl

e,pa

per,

card

boar

d,to

oth

pick

s,gu

mdr

ops.

See

stu

den

ts’w

ork

.

wid

th

wid

thle

ngth

leng

th

dept

h

5MG

2.3,

6M

R2.

4



Dra

w a

top

,a s

ide,

and

a f

ron

t vi

ew o

f ea

ch s

olid

.

1.2.

3.4.

Dra

w e

ach

sol

id w

hos

e to

p,s

ide,

and

fro

nt

view

s ar

e sh

own

.Use

isom

etri

c d

ot p

aper

.

1.2.

7.H

AT

RA

CK

Dra

w a

top

,a s

ide,

and

a fr

ont

view

of

the

hat

rac

k sh

own

.

8.M

USI

CS

ketc

h v

iew

s of

th

e to

p,si

de,a

nd

fron

t of

th

e pi

ano

show

n.

fron

t s

ide

top

fron

t s

ide

top

fron

t s

ide

top

fron

t s

ide

top

fron

t s

ide

top

fron

t s

ide

top

fron

t s

ide

top

fron

t s

ide

top

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

11

55G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–8

pygp

11-8

5MG

2.3,

6M

R2.

4Pr

actic

eD

raw

ing

Th

ree-

Dim

ensi

on

al F

igu

res

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

11

54G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6


11-8

Dra

w a

top

,a s

ide,

and

a f

ron

t vi

ew o

f ea

ch s

olid

.

1. 2. 3.

Dra

w e

ach

sol

id u

sin

g th

e to

p,s

ide,

and

fro

nt

view

s sh

own

.Use

isom

etri

c d

ot p

aper

.

4. 5.to

psid

efro

nt

top

side

front

top

side

front

top

side

front

top

side

front

5MG

2.3,

6M

R2.

4Sk

ills

Prac

tice

Dra

win

g T

hre

e-D

imen

sio

nal

Fig

ure

s



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

11

57G

lenc

oe C

alifo

rnia

Mat

hem

atic

s, G

rade

6

Lesson 11–8

pygp

11-8

Co

un

tin

g C

ub

esT

he

figu

res

on t

his

pag

e h

ave

been

bu

ilt

by g

luin

g cu

bes

toge

ther

.Use

you

rvi

sual

im

agin

atio

n t

o co

un

t th

e to

tal

nu

mbe

r of

cu

bes

as w

ell

as t

he

nu

mbe

rof

cu

bes

wit

h g

lue

on 1

,2,3

,4,o

r 5,

or 6

fac

es.

Com

ple

te t

his

ch

art

for

the

figu

res

bel

ow.

1.2.

3.

4.5.

6.

Tot

al

Nu

mb

er o

f F

aces

wit

h G

lue

on T

hem

Fig

ure

Nu

mb

er

of C

ub

es1

face

2 fa

ces

3 fa

ces

4 fa

ces

5 fa

ces

6 fa

ces

113

03

72

10

217

01

86

20

314

50

80

10

436

00

1620

00

522

46

64

20

635

12

916

61

5MG

2.3,

6M

R2.

4

NA

ME

____

____

____

____

____

____

____

____

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____

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56G

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11-8

1.A

RC

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11-9

Get

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on

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i L

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t th

e to

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our

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k.W

rite

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elow

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hat

is

the

area

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the

base

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e bo

x? W

hat

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the

hei

ght

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cm2 ;

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ow m

any

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bes

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box?

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3.W

hat

do

you

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ice

abou

t th

e pr

odu

ct o

f th

e ba

se a

rea

and

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hei

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eq

ual

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hat

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? W

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is t

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oth

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rec

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ple

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me

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ds.

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ple

answ

er:

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ltip

ly t

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len

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tim

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.

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6MG

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oun

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if

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7.8.

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ESTI

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TIO

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stim

ate

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ALG

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NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

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____

____

____

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ER

IOD

__

___

Prac

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of

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11

61G

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hem

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____

____

____

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Skill

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11-9

Fin

d t

he

volu

me

of e

ach

rec

tan

gula

r p

rism

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nd

to

the

nea

rest

ten

th i

f n

eces

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.

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m5

mm12

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4 m

4 m

6 m

6 in

.

10 in

.

5 in

.

7 cm

3 cm

3 cm

6MG

1.3



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

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11

63G

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hem

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Lesson 11–9

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Vo

lum

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wit

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e ba

se a

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are

show

n b

elow

.

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e ex

erci

ses

on t

his

pag

e w

ill

hel

p yo

u d

isco

ver

how

th

eir

volu

mes

are

rela

ted.

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larg

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tern

s b

elow

to

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e th

e op

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en p

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own

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sid

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me.

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our

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any

tim

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ust

you

do

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to

fill

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en p

rism

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es

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wou

ld f

ind

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volu

me

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mid

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own

at

the

righ

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ivid

e th

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lum

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f a

pri

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ith

the

sam

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ase

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ener

aliz

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tate

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for

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p

6MG

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NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

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of

Pri

sms

Cha

pter

11

62G

lenc

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alifo

rnia

Mat

hem

atic

s, G

rade

6


11-9

1.PA

CK

AG

ING

A c

erea

l bo

x h

as a

len

gth

of

8 in

ches

,a w

idth

of

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inch

es,a

nd

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ght

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2 �1 8�

inch

es.W

hat

is

the

volu

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cere

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ox?

169 �

3 4�in

3

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OD

STO

RA

GE

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ants

to

dete

rmin

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uch

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it

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l ta

ke t

ofi

ll h

er c

oole

r.If

th

e co

oler

has

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engt

hof

22

inch

es,a

wid

th o

f 12

in

ches

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d a

hei

ght

of 1

0 �1 2�

inch

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ow m

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l

her

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ler

hol

d?2,

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AN

SPO

RTA

TIO

NT

he

carg

o-ca

rryi

ng

part

of

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ly’s

tru

ck h

as a

len

gth

of

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met

ers,

a w

idth

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3 m

eter

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hei

ght

of 4

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eter

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hat

is

the

max

imu

m v

olu

me

of s

and

that

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ly’s

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ck c

an c

arry

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4.58

m3

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UM

BIN

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lexi

a’s

bath

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ub

in t

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shap

e of

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ngu

lar

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ith

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h o

f 1.

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ght

of 0

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eter

.H

ow m

any

cubi

c fe

et o

f w

ater

can

it

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3

5.PA

CK

AG

ING

A b

ox o

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ssu

es h

as a

len

gth

of

11.2

cen

tim

eter

s,a

wid

th o

f11

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enti

met

ers,

and

a h

eigh

t of

13 c

enti

met

ers.

Wh

at i

s th

e vo

lum

e of

the

tiss

ue

box?

1,

630.

72 c

m3

6.G

EOM

ETRY

A p

enta

gon

al p

rism

is a

pris

m t

hat

has

bas

es t

hat

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pen

tago

ns.

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Bh

wh

ere

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th

ear

ea o

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se,t

o fi

nd

the

volu

me

ofth

e pe

nta

gon

al p

rism

bel

ow. 11

8.35

cm

3

4.5

cm

B =

26.3

cm

26MG

1.3



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Less

on R

eadi

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uide

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me

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Cha

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65G

lenc

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hem

atic

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Get

Rea

dy

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Less

on

Com

ple

te t

he

Min

i L

ab a

t th

e to

p o

f p

age

619

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.E

stim

ate

the

nu

mbe

r of

cen

tim

eter

cu

bes

that

wou

ld f

it a

t th

e bo

ttom

of

the

can

.In

clu

de p

arts

of

cube

s.S

ee s

tud

ents

’wo

rk.

2.H

ow m

any

laye

rs w

ould

it

take

to

fill

th

e cy

lin

der?

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stu

den

ts’w

ork

.

3.M

AK

E A

CO

NJE

CTU

RE

abou

t h

ow y

ou c

an f

ind

the

volu

me

of t

he

sou

p ca

n.

Sam

ple

an

swer

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ult

iply

th

e ar

ea o

f th

e b

ase

and

th

e h

eig

ht.

Rea

din

g t

he

Less

on

4.W

rite

Cif

th

e ph

rase

is

tru

e of

a c

ylin

der,

Pif

th

e ph

rase

is

tru

e of

apr

ism

,or

CP

if t

he

phra

se i

s tr

ue

of b

oth

.

has

bas

es t

hat

are

par

alle

l an

d co

ngr

uen

t

has

sid

es a

nd

base

s th

at a

re p

olyg

ons

has

bas

es t

hat

are

cir

cula

r

is a

sol

id

has

vol

um

e

is t

hre

e-di

men

sion

al

5.W

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ape

is t

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hat

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the

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ake

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nd

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you

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dric

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xch

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obj

ects

wit

h y

our

part

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t do

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sh

are

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calc

ula

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eter

min

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obj

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en c

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11-9

To

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me

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ula

an

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for

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1.2.

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4.C

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LLEN

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Supp

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you

need

a r

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ar p

rism

with

leng

th 4

inch

es a

nd w

idth

3.5

inch

es

and

a vo

lum

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140

cub

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ches

. Wha

t hei

ght m

ust t

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rism

hav

e?10

inch

es

3.29

cm

1.74

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5.67

cm

15 y

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11 y

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EN

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EN

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Exam

ple

4.6

cm2.

5 cm

7.1

cm

3.5

cm3

3,46

5 yd

332

.5 c

m3

Answers (Lessons 11-9 and 11-10)


NA

ME

____

____

____

____

____

____

____

____

____

____

DA

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67G

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hem

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6

Lesson 11–10

pygp

11-1

0

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d t

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me

of e

ach

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ind

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se 3

.14

for π.

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nd

to

the

nea

rest

ten

th.

1.2.

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3,07

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cm3

1,80

8.6

ft3

150.

7 in

3

4.5.

6.

230.

8 yd

319

1.8

m3

70.3

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radi

us

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125.

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3

9.di

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.di

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hei

ght

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314.

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6.2

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5.3

m

8.7

m

3

yd

6 yd1 2

12 in

.4

in.

8 ft

9 ft

7 cm 20

cm

6MG

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____

____

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____

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____

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and

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0

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.

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esti

mat

ion

.

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d t

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volu

me

of e

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ind

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.14

for π.

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nd

to

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nea

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ten

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3.

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mm

364

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diam

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diam

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m

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m3

2 in

. 2 in

.

4 ft

12.9

ft

10 m

m 18 m

m

2 in

. 5 in

.

As

with

pris

ms,

the

are

a of

the

bas

e of

a c

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der

tells

the

num

ber

of c

ubic

uni

ts in

one

laye

r.T

hehe

ight

tel

ls h

ow m

any

laye

rs t

here

are

in t

he c

ylin

der.

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vol

ume

Vof

a c

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with

rad

ius

ris

the

area

of

the

base

Btim

es t

he h

eigh

t h.

V �

Bh

or V

= �

r2h,

whe

re B

��

r2

r

h

B =

�r2

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ple

6MG

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____

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pygp

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ATE

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cyl

indr

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wat

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nk

has

a d

iam

eter

of

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met

ers

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a h

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9 m

eter

s.W

hat

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the

max

imu

m v

olu

me

that

th

e w

ater

tan

kca

n h

old?

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nd

to t

he

nea

rest

ten

th.

198.

5 m

3

2.PA

CK

AG

ING

A c

an o

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as a

diam

eter

of

6.6

cen

tim

eter

s an

d a

hei

ght

of 9

.9 c

enti

met

ers.

How

mu

chco

rn c

an t

he

can

hol

d? R

oun

d to

th

en

eare

st t

enth

.33

8.5

cm3

3.C

ON

TAIN

ERS

Tio

nn

a w

ants

to

dete

rmin

eth

e m

axim

um

cap

acit

y of

a c

ylin

dric

albu

cket

th

at h

as a

rad

ius

of 6

in

ches

and

a h

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t of

12

inch

es.W

hat

is

the

capa

city

of T

ion

na’

s bu

cket

? R

oun

d to

the

nea

rest

ten

th.

1,35

6.5

in3

4.D

ESIG

NR

odol

fo i

s de

sign

ing

a n

ew,

cyli

ndr

ical

dri

nki

ng

glas

s.If

th

e gl

ass

has

a d

iam

eter

of

8 ce

nti

met

ers

and

ah

eigh

t of

12.

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nti

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wh

at i

s it

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lum

e? R

oun

d to

th

e n

eare

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enth

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3.1

cm3

5.PA

INT

A c

an o

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int

is 1

5 ce

nti

met

ers

hig

h a

nd

has

a d

iam

eter

of

13.6

cm

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hat

is

the

volu

me

of t

he

can

? R

oun

dto

th

e n

eare

st t

enth

.2,

177.

9 cm

3

6.SP

ICES

A s

pice

man

ufa

ctu

rer

use

s a

cyli

ndr

ical

dis

pen

ser

like

th

e on

esh

own

.Fin

d th

e vo

lum

e of

th

edi

spen

ser

to t

he

nea

rest

ten

th. 27

.2 in

31.

7 in

. 3 in

.

6MG

1.3

Fin

d t

he

volu

me

of e

ach

cyl

ind

er.U

se 3

.14

for π.

Rou

nd

to

the

nea

rest

ten

th.

1.2.

3.

471.

0 ft

31,

692.

5 m

31,

017.

4 yd

3

4.5.

6.

1,15

5.5

in3

358.

9 m

m3

58.2

cm

3

7.ra

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3.7

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diam

eter

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CO

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Wh

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arre

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as a

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MA

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eac

h c

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der

wit

h i

ts a

pp

roxi

mat

e vo

lum

e.

11.

diam

eter

�4

cm,h

eigh

t �

3.6

cmd

.a.

108

ft3

12.

radi

us

�2.

7 cm

,hei

ght

�5

cmb

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ft3

13.

radi

us

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c.96

ft3

14.

diam

eter

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2 cm

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d.

48 f

t3

15.

FUEL

Tw

o fu

el t

anks

wit

h t

he

dim

ensi

ons

show

n h

ave

the

sam

e vo

lum

e.W

hat

is

the

valu

e of

h?

2 ft

6 ft

h

8 ft

3 ft

4.2c

m

2.1c

m3

mm

12.7

mm

8 in

.

23 in

.

9 yd

4 yd

14 m

11 m

10 ft

6 ft

NA

ME

____

____

____

____

____

____

____

____

____

____

DA

TE

___

____

____

___

PE

RIO

D

____

_

Prac

tice

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me

of

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ind

ers

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pter

11

68G

lenc

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alifo

rnia

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hem

atic

s, G

rade

6


11-1

06M

G1.

3



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

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ER

IOD

__

___

Enri

chm

ent

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11

70G

lenc

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hem

atic

s, G

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11-1

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Vo

lum

es o

f N

on

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sIm

agin

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stac

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ten

pen

nie

s.B

y pu

shin

g ag

ain

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he

stac

k,yo

u c

an c

han

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ts s

hap

e as

sh

own

at

the

righ

t.B

ut,

the

volu

me

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k do

es n

ot c

han

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agra

ms

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w s

how

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h

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the

sam

e vo

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me

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se 3

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1.2.

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6.

180

yd3

125.

6 cm

324

0 cm

3

15

cm

4 c

m

4 c

m1

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m

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m

10

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d

3 y

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7 y

d

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10

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.

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.

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11

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.

2 i

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6MG

1.3




Chapter 11 Assessment Answer KeyQuiz 1 (Lessons 11-1 and 11-3) Quiz 3 (Lessons 11-6 and 11-8) Mid-Chapter TestPage 73 Page 74 Page 75

An

swer

s

Cop

yrig

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Gle

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raw

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, a

divi

sion

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cGra

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, In

c.

Quiz 2 (Lessons 11-4 and 11-5)

Page 73

Quiz 4 (Lessons 11-9 and 11-10)

Page 74

1.

2.

3.

4.

5. C

113.0 mm2

50.2 in2

10.2 cm2

20.3 ft2

1.

2.

3.

4.

5.

top side front

topside front

triangular prism

25 in2

76.8 ft2

1.

2.

3.

4.

5. 949.9 in3

16,328.0 cm3

854.1 yd3

2,200 mm3

518.4 ft3

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. 89.2 cm

14.1 yd

55.9 cm2

20.25 ft2

33 cm2

C

G

C

F

C1.

2.

3.

4.

5. 31.4 mm

792 ft2

3,840 m2

663 ft2

38.3 m2

Chapter 11 Assessment Answer KeyVocabulary Test Form 1Page 76 Page 77 Page 78


Copyright ©

Glencoe/M

cGraw


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raw-H

ill Com

panies, Inc.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Sample answer: thesides of a three-dimensional figure

Sample answer: a figure that ismade up of various two-dimensional figures

c

d

c

h

g

b

a

g

e

f 12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 9.5 m

H

B

G

D

H

A

G

D

G1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. A

H

B

G

C

H

B

G

C

G

A


An

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Cop

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Gle

ncoe

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raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.Chapter 11 Assessment Answer Key

Form 2A Form 2BPage 79 Page 80 Page 81 Page 82

1.

2.

3.

4.

5.

6.

7.

8.

9. C

G

C

F

A

G

B

G

B 10.

11.

12.

13.

14.

15.

16.

B: 13.3 mm

J

C

H

A

H

D

H 1.

2.

3.

4.

5.

6.

7.

8.

9. B

G

B

J

D

G

D

H

B 10.

11.

12.

13.

14.

15.

16.

B: 20 in.

F

B

F

D

G

A

H


Chapter 11 Assessment Answer KeyForm 2CPage 83 Page 84

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.pentagon;

pentagonal pyramid

113.0 in3

907.5 in2

113.0 cm2

288 mi2

476.6 m2

108 mm2

32 ft2

59.7 ft

80.4 cm

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 810 ft3

282.6 yd3

1,361.5 cm3

565.2 m3

76.7 in3

1,800 mm3

390 in3

top side front

top side front

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

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of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.


An

swer

s

Chapter 11 Assessment Answer KeyForm 2DPage 85 Page 86

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

triangle; triangularprism

56.5 in3

615.4 in2

38.5 ft2

576 cm2

57.1 in2

500 mm2

36 m2

29.8 in.

17.0 mm

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 53.3 yd3

1,077.0 cm3

67,794.6 mm3

4,421.1 ft3

6,335.6 mm3

6,384 in3

672 cm3

top side front

top side front

Copyright ©

Glencoe/M

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ill Com

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Chapter 11 Assessment Answer KeyForm 3Page 87 Page 88

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.hexagon; hexagonal

prism

4,534.2 m3

1,169.6 m2

7,850.0 ft2

900 cm2

138.4 ft2

360 m2

160 cm2

56.5 in.

23.9 yd

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 614.1 ft3

15,878.4 in3

5,342.2 cm3

6,217.2 in3

1,008.2 m3

2,060.0 ft3

5,760 mm3

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Chapter 11 Assessment Answer KeyPage 89, Extended-Response Test

Scoring Rubric

Level Specific Criteria

4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.

3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.

2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.

1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.

0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.

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Chapter 11 Assessment Answer Key Page 89, Extended-Response Test

Sample AnswersIn addition to the scoring rubric found on page A39, the following sample answers may be used as guidance in evaluating extended-response assessment items.

1. a. Use isometric drawings to drawthree-dimensional figures.

OR

Draw the top, side, and front views ofthree-dimensional figures.

b.

c.

d.

2. The volumes of both a prism and acylinder are given by the area of thebase times the height.

3a. 12 � 2� � 2w

If the length is 4, 12 � 2(4) � 2w

2 � w

The dimensions of the rectanglecould be 4 cm � 2 cm.

12 � 2�r

6 � 3.14r

1.9 � r

The radius of the circle is about 1.9 cm.

3b. � � 6�12

� cm P � C

w � 2�23

� cm

P � 2(�132�) � 2(�

83

�)P � �

535� � 18�

13

� � C

�535� � 2(3.14)r

r � 2.9 cm

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c.Chapter 11 Assessment Answer Key

Standardized Test PracticePage 90 Page 91

1.

2.

3.

4.

5.

6.

7.

8. F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D 9.

10.

11.

12.

13.

14.

15.

16. F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D


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Standardized Test PracticePage 92

17.

18.

19.

20.

21.

22.

23.

24.

25a.

25b.

Sample answer;diameter 15 inches,height 12 inches V � �r2h � � (7.5)2

(12) � 2,120 in3

V � 10 � 12 � 50 � 6,000 in3

2,059.8 yd3

10.3 ft3

top side front

$1.59

36

0.35

30, 36, 42

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