chapter 13 resource masters - math problem solving©glencoe/mcgraw-hill iv glencoe geometry...
TRANSCRIPT
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks.
Study Guide and Intervention Workbook 0-07-860191-6Skills Practice Workbook 0-07-860192-4Practice Workbook 0-07-860193-2Reading to Learn Mathematics Workbook 0-07-861061-3
ANSWERS FOR WORKBOOKS The answers for Chapter 13 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Geometry. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
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ISBN: 0-07-860190-8 GeometryChapter 13 Resource Masters
1 2 3 4 5 6 7 8 9 10 009 11 10 09 08 07 06 05 04 03
© Glencoe/McGraw-Hill iii Glencoe Geometry
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 13-1Study Guide and Intervention . . . . . . . . 723–724Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 725Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 726Reading to Learn Mathematics . . . . . . . . . . 727Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 728
Lesson 13-2Study Guide and Intervention . . . . . . . . 729–730Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 731Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 732Reading to Learn Mathematics . . . . . . . . . . 733Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 734
Lesson 13-3Study Guide and Intervention . . . . . . . . 735–736Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 737Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 738Reading to Learn Mathematics . . . . . . . . . . 739Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 740
Lesson 13-4Study Guide and Intervention . . . . . . . . 741–742Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 743Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 744Reading to Learn Mathematics . . . . . . . . . . 745Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 746
Lesson 13-5Study Guide and Intervention . . . . . . . . 747–748Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 749Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 750Reading to Learn Mathematics . . . . . . . . . . 751Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 752
Chapter 13 AssessmentChapter 13 Test, Form 1 . . . . . . . . . . . 753–754Chapter 13 Test, Form 2A . . . . . . . . . . 755–756Chapter 13 Test, Form 2B . . . . . . . . . . 757–758Chapter 13 Test, Form 2C . . . . . . . . . . 759–760Chapter 13 Test, Form 2D . . . . . . . . . . 761–762Chapter 13 Test, Form 3 . . . . . . . . . . . 763–764Chapter 13 Open-Ended Assessment . . . . . 765Chapter 13 Vocabulary Test/Review . . . . . . 766Chapter 13 Quizzes 1 & 2 . . . . . . . . . . . . . . 767Chapter 13 Quizzes 3 & 4 . . . . . . . . . . . . . . 768Chapter 13 Mid-Chapter Test . . . . . . . . . . . . 769Chapter 13 Cumulative Review . . . . . . . . . . 770Chapter 13 Standardized Test Practice 771–772Unit 4 Test/Review (Ch. 4–7) . . . . . . . . 773–774Second Semester Test (Ch. 8–13) . . . . 775–778Final Test . . . . . . . . . . . . . . . . . . . . . . 779–784
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A32
© Glencoe/McGraw-Hill iv Glencoe Geometry
Teacher’s Guide to Using theChapter 13 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 13 Resource Masters includes the core materialsneeded for Chapter 13. These materials include worksheets, extensions, andassessment options. The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theGeometry TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 13-1.Encourage them to add these pages to theirGeometry Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Geometry addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Geometry
Assessment OptionsThe assessment masters in the Chapter 13Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Geometry. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of geometry conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and short-responsequestions. Bubble-in and grid-in answersections are provided on the master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 724–725. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
1313
© Glencoe/McGraw-Hill vii Glencoe Geometry
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 13. As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Geometry Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
congruent solids
ordered triple
similar solids
volume
Study Guide and InterventionVolumes of Prisms and Cylinders
NAME ______________________________________________ DATE ____________ PERIOD _____
13-113-1
© Glencoe/McGraw-Hill 723 Glencoe Geometry
Less
on
13-
1
Volumes of Prisms The measure of the amount of space that a three-dimensional figure encloses is the volume of the figure. Volume is measured in units such as cubic feet, cubic yards, or cubic meters. One cubic unit is the volume of a cube that measures one unit on each edge.
27 cubic feet � 1 cubic yard
Volume If a prism has a volume of V cubic units, a height of h units, of a Prism and each base has an area of B square units, then V � Bh.
cubic foot cubic yard
Find the volume of the prism.
V � Bh Formula for volume
� (7)(3)(4) B � (7)(3), h � 4
� 84 Multiply.
The volume of the prism is 84 cubiccentimeters.
7 cm3 cm
4 cm
Find the volume of theprism if the area of each base is 6.3square feet.
V � Bh Formula for volume
� (6.3)(3.5) B � 6.3, h � 3.5
� 22.05 Multiply.
The volume is 22.05 cubic feet.
3.5 ft
base
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find the volume of each prism. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
7 yd4 yd
3 yd
4 cm
6 cm
2 cm
1.5 cm
10 ft15 ft
12 ft
30�15 ft
12 ft
3 cm
4 cm
1.5 cm
8 ft
8 ft
8 ft
© Glencoe/McGraw-Hill 724 Glencoe Geometry
Volumes of Cylinders The volume of a cylinder is the product of the height and the area of the base. The base of a cylinder is a circle, so the area of the base is �r2.
Volume of If a cylinder has a volume of V cubic units, a height of h units, a Cylinder and the bases have radii of r units, then V � �r 2h.
r
h
Study Guide and Intervention (continued)
Volumes of Prisms and Cylinders
NAME ______________________________________________ DATE ____________ PERIOD _____
13-113-1
Find the volume of the cylinder.
V � �r2h Volume of a cylinder
� �(3)2(4) r � 3, h � 4
� 113.1 Simplify.
The volume is about 113.1 cubiccentimeters.
4 cm
3 cm
Find the area of the oblique cylinder.
The radius of each base is 4 inches, so the area ofthe base is 16� in2. Use the Pythagorean Theoremto find the height of the cylinder.
h2 � 52 � 132 Pythagorean Theorem
h2 � 144 Simplify.
h � 12 Take the square root of each side.
V � �r2h Volume of a cylinder
� �(4)2(12) r � 4, h �12
� 603.2 in3 Simplify.
8 in.
13 in.
5 in.
h
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find the volume of each cylinder. Round to the nearest tenth.
1. 2.
3. 4.
5. 6.
1 yd4 yd
10 cm
13 cm
20 ft
20 ft12 ft1.5 ft
18 cm2 cm2 ft
1 ft
Skills PracticeVolumes of Prisms and Cylinders
NAME ______________________________________________ DATE ____________ PERIOD _____
13-113-1
© Glencoe/McGraw-Hill 725 Glencoe Geometry
Less
on
13-
1
Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
Find the volume of each oblique prism or cylinder. Round to the nearest tenth ifnecessary.
7. 8.
5 in.
3 in.17 cm
18 cm
4 cm
6 yd
10 yd15 mm23 mm
16 in. 22 in.
34 in.
3 m
5 m
13 m
6 ft
8 ft
2 ft
18 cm
16 cm
8 cm
© Glencoe/McGraw-Hill 726 Glencoe Geometry
Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
AQUARIUM For Exercises 7–9, use the following information. Round answers tothe nearest tenth.Mr. Gutierrez purchased a cylindrical aquarium for his office. The aquarium has a height of 25�
12� inches and a radius of 21 inches.
7. What is the volume of the aquarium in cubic feet?
8. If there are 7.48 gallons in a cubic foot, how many gallons of water does the aquariumhold?
9. If a cubic foot of water weighs about 62.4 pounds, what is the weight of the water in theaquarium to the nearest five pounds?
30 cm
8 cm
13 yd
20 yd
10 yd
7 ft 25 ft16 mm 17.5 mm
5 in.
5 in.
5 in.
9 in.17 m
10 m
26 m
Practice Volumes of Prisms and Cylinders
NAME ______________________________________________ DATE ____________ PERIOD _____
13-113-1
Reading to Learn MathematicsVolumes of Prisms and Cylinders
NAME ______________________________________________ DATE ____________ PERIOD _____
13-113-1
© Glencoe/McGraw-Hill 727 Glencoe Geometry
Less
on
13-
1
Pre-Activity How is mathematics used in comics?
Read the introduction to Lesson 13-1 at the top of page 688 in your textbook.
In the cartoon, why was Shoe confused when the teacher said the class wasgoing to discuss volumes?
Reading the Lesson1. In each case, write a formula for the volume V of the solid in terms of the given variables.
a. a rectangular box with length a, width b, and height c
b. a rectangular box with square bases with side length x, and with height y
c. a cube with edges of length e
d. a triangular prism whose bases are isosceles right triangles with legs of length x, andwhose height is y
e. a prism whose bases are regular polygons with perimeter P and apothem a, andwhose height is h
f. a cylinder whose bases each have radius r, and whose height is three times the radiusof the bases
g. a regular octagonal prism in which each base has sides of length s and apothem a,and whose height is t
h. a cylinder with height h whose bases each have diameter d
i. an oblique cylinder whose bases have radius a and whose height is b
j. a regular hexagonal prism whose bases have side length s, and whose height is h
Helping You Remember2. A good way to remember a mathematical concept is to explain it to someone else. Suppose
that your younger sister, who is in eighth grade, is having trouble understanding whysquare units are used to measure area, but cubic units are needed to measure volume.How can you explain this to her in a way that will make it easy for her to understandand remember the correct units to use?
© Glencoe/McGraw-Hill 728 Glencoe Geometry
Visible Surface Area
Use paper, scissors, and tape to make five cubes that have one-inch edges.Arrange the cubes to form each shape shown. Then find the volume and the visible surface area. In other words, do not include the area of surfacecovered by other cubes or by the table or desk.
1. 2.
volume � volume �
surface area � surface area �
3. 4. 5.
volume � volume � volume �
surface area � surface area � surface area �
6. Find the volume and the visible surface area of the figure at the right.
volume �
surface area �
4 in.
4 in.
3 in.
3 in.
3 in.
8 in.
3 in.
5 in.
5 in.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
13-113-1
Study Guide and InterventionVolumes of Pyramids and Cones
NAME ______________________________________________ DATE ____________ PERIOD _____
13-213-2
© Glencoe/McGraw-Hill 729 Glencoe Geometry
Less
on
13-
2
Volumes of Pyramids This figure shows a prism and a pyramid that have the same base and the same height. It is clear that the volume of the pyramid is less than the volume of the prism. More specifically,the volume of the pyramid is one-third of the volume of the prism.
Volume of If a pyramid has a volume of V cubic units, a height of h units, a Pyramid and a base with an area of B square units, then V � �1
3�Bh.
Find the volume of the square pyramid.
V � �13�Bh Volume of a pyramid
� �13�(8)(8)10 B � (8)(8), h � 10
� 213.3 Multiply.
The volume is about 213.3 cubic feet.
Find the volume of each pyramid. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6. 6 yd
8 yd
5 yd15 in.
15 in.
16 in.
18 ft
regularhexagon 6 ft
4 cm8 cm
12 cm
10 ft
6 ft15 ft
12 ft
8 ft
10 ft
8 ft
8 ft
10 ft
ExercisesExercises
ExampleExample
© Glencoe/McGraw-Hill 730 Glencoe Geometry
Volumes of Cones For a cone, the volume is one-third the product of the height and the base. The base of a cone is a circle, so the area of the base is �r2.
Volume of a Right If a cone has a volume of V cubic units, a height of h units, Circular Cone and the area of the base is B square units, then V � �1
3�Bh.
The same formula can be used to find the volume of oblique cones.
Find the volume of the cone.
V � �13��r2h Volume of a cone
� �13��(5)212 r � 5, h � 12
� 314.2 Simplify.
The volume of the cone is about 314.2 cubic centimeters.
Find the volume of each cone. Round to the nearest tenth.
1. 2.
3. 4.
5. 6.
16 cm
45�26 ft
20 ft
45�18 yd
20 yd30 in.
12 in.
8 ft
10 ft6 cm10 cm
12 cm
5 cm
r
h
Study Guide and Intervention (continued)
Volumes of Pyramids and Cones
NAME ______________________________________________ DATE ____________ PERIOD _____
13-213-2
ExercisesExercises
ExampleExample
Skills PracticeVolumes of Pyramids and Cones
NAME ______________________________________________ DATE ____________ PERIOD _____
13-213-2
© Glencoe/McGraw-Hill 731 Glencoe Geometry
Less
on
13-
2
Find the volume of each pyramid or cone. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
Find the volume of each oblique pyramid or cone. Round to the nearest tenth ifnecessary.
7. 8.
12 cm
6 cm
4 ft4 ft
6 ft
66�18 mm
25 yd
14 yd
25 m
12 m
8 in.10 in.
14 in.
4 cm7 cm
8 cm
5 ft5 ft
8 ft
© Glencoe/McGraw-Hill 732 Glencoe Geometry
Find the volume of each pyramid or cone. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
7. CONSTRUCTION Mr. Ganty built a conical storage shed. The base of the shed is 4 metersin diameter, and the height of the shed is 3.8 meters. What is the volume of the shed?
8. HISTORY The start of the pyramid age began with King Zoser’s pyramid, erected in the27th century B.C. In its original state, it stood 62 meters high with a rectangular basethat measured 140 meters by 118 meters. Find the volume of the original pyramid.
37 ft11 ft
6 in.6 in.
11 in.
52�12 mm19 ft
9 ft
12.5 cm25 cm
23 cm
9.2 yd9.2 yd
13 yd
Practice Volumes of Pyramids and Cones
NAME ______________________________________________ DATE ____________ PERIOD _____
13-213-2
Reading to Learn MathematicsVolumes of Pyramids and Cones
NAME ______________________________________________ DATE ____________ PERIOD _____
13-213-2
© Glencoe/McGraw-Hill 733 Glencoe Geometry
Less
on
13-
2
Pre-Activity How do architects use geometry?
Read the introduction to Lesson 13-2 at the top of page 696 in your textbook.
In addition to reflecting more light, why do you think the architect of theTransamerica Pyramid may have designed the building as a square pyramidrather than a rectangular prism?
Reading the Lesson1. In each case, two solids are described. Determine whether the first solid or the second
solid has the greater volume, or if the two solids have the same volume. (Answer bywriting first, second, or same.)a. First solid: A rectangular prism with length x, width y, and height z
Second solid: A rectangular prism with length 2x, width y, height zb. First solid: a rectangular prism that has a square base with side length x and that
has height ySecond solid: a square pyramid whose base has side length x and that has height y
c. First solid: a right cone whose base has radius x and that has height ySecond solid: an oblique cone whose base has radius x and that has height y
d. First solid: a cone whose base has radius x, and whose height is ySecond solid: a cylinder whose bases have radius x, and whose height is y
e. First solid: a cone whose base has radius x and whose height is ySecond solid: a square pyramid whose base has side length x and whose height is y
2. Supply the missing numbers to form true statements.
a. If the length, width, and height of a rectangular box are all doubled, its volume will
be multiplied by .
b. If the radius of a cylinder is tripled and the height is unchanged, the volume will be
multiplied by .
c. In a square pyramid, if the side length of the base is multiplied by 1.5 and the height
is doubled, the volume will be multiplied by .
d. In a cone, if the radius of the base is tripled and the height is doubled, the volume
will be multiplied by .
e. In a cube, if the edge length is multiplied by 5, the volume will be multiplied by .
Helping You Remember
3. Many students find it easier to remember mathematical formulas if they can put themin words. Use words to describe in one sentence how to find the volume of any pyramidor cylinder.
© Glencoe/McGraw-Hill 734 Glencoe Geometry
FrustumsA frustum is a figure formed when a plane intersects a pyramid orcone so that the plane is parallel to the solid’s base. The frustum is the part of the solid between the plane and the base. To find thevolume of a frustum, the areas of both bases must be calculated andused in the formula
V � �13
�h(B1 � B2 � �B1B2�),where h � height (perpendicular distance between the bases),B1 � area of top base, and B2 � area of bottom base.
Describe the shape of the bases of each frustum. Then find the volume. Round to the nearest tenth.
1. 2.
3. 4.
12 ft13 ft
7 ft8 m
6 m
12 m
4.5 m2.25 m
3 m
5 m
3 in.
7.5 in.
4.5 in.
13 cm
6 cm
9 cm
5 cm
19.5 cm
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
13-213-2
Study Guide and InterventionVolumes of Spheres
NAME ______________________________________________ DATE ____________ PERIOD _____
13-313-3
© Glencoe/McGraw-Hill 735 Glencoe Geometry
Less
on
13-
3
Volumes of Spheres A sphere has one basic measurement, the length of its radius. If you know the radius of a sphere, you can calculate its volume.
Volume of a Sphere
If a sphere has a volume of V cubic units and a radius of r units, then V � �43
��r 3.
Find the volume of a sphere with radius 8 centimeters.
V � �43��r3 Volume of a sphere
� �43��(8)3 r � 8
� 2144.7 Simplify.
The volume is about 2144.7 cubic centimeters.
A sphere with radius 5 inches just fits inside a cylinder. What is the difference between the volume of thecylinder and the volume of the sphere? Round to the nearest cubic inch.The base of the cylinder is 25� in2 and the height is 10 in., so the volume of the cylinder is 250� in3. The volume of the sphere is �
43��(5)3
or �5030�� in3. The difference in the volumes is 250� � �
5030�� or about 262 in3.
Find the volume of each solid. Round to the nearest tenth.
1. 2. 3.
4. 5. 6.
7. A hemisphere with radius 16 centimeters just fits inside a rectangular prism. What isthe difference between the volume of the prism and the volume of the hemisphere?Round to the nearest cubic centimeter.
8 in. difference between volume of cube and volume of sphere
13 in.5 in.
8 cm
16 in.
6 in.
5 ft
5 in.
5 in.
5 in.5 in.
8 cm
r
ExercisesExercises
Example 1Example 1
Example 2Example 2
© Glencoe/McGraw-Hill 736 Glencoe Geometry
Solve Problems Involving Volumes of Spheres If you want to know if a spherecan be packed inside another container, or if you want to compare the capacity of a sphereand another shape, you can compare volumes.
Compare the volumes of the sphere and the cylinder. Determine which quantity is greater.
V � �43��r3 Volume of sphere V � �r2h Volume of cylinder
� �r2(1.5r) h � 1.5r
� 1.5�r3 Simplify.
Compare �43��r3 with 1.5�r3. Since �
43� is less than 1.5, it follows that
the volume of the sphere is less than the volume of the cylinder.
Compare the volume of a sphere with radius r to the volume of each figure below.Which figure has a greater volume?
1. 2.
3. 4.
5. 6.2a
r
3r
r
r3r
r
rr
rr2
2r
r1.5r
Study Guide and Intervention (continued)
Volumes of Spheres
NAME ______________________________________________ DATE ____________ PERIOD _____
13-313-3
ExercisesExercises
ExampleExample
Skills PracticeVolumes of Spheres
NAME ______________________________________________ DATE ____________ PERIOD _____
13-313-3
© Glencoe/McGraw-Hill 737 Glencoe Geometry
Less
on
13-
3
Find the volume of each sphere or hemisphere. Round to the nearest tenth.
1. The radius of the sphere is 9 centimeters.
2. The diameter of the sphere is 10 inches.
3. The circumference of the sphere is 26 meters.
4. The radius of the hemisphere is 7 feet.
5. The diameter of the hemisphere is 12 kilometers.
6. The circumference of the hemisphere is 48 yards.
7. 8.
9. 10.
14.4 m
4.5 in.
94.8 ft16.2 cm
© Glencoe/McGraw-Hill 738 Glencoe Geometry
Find the volume of each sphere or hemisphere. Round to the nearest tenth.
1. The radius of the sphere is 12.4 centimeters.
2. The diameter of the sphere is 17 feet.
3. The circumference of the sphere is 38 meters.
4. The diameter of the hemisphere is 21 inches.
5. The circumference of the hemisphere is 18 millimeters.
6. 7.
8. 9.
10. PACKAGING Amber plans to ship a mini-basketball she bought for her nephew. Thecircumference of the ball is 24 inches and the package she wants to ship it in is arectangular box that measures 8 inches � 8 inches � 9 inches. Will the basketball fit inthe box? Explain.
C � 43 mm
32 m
C � 58 cm12.32 ft
Practice Volumes of Spheres
NAME ______________________________________________ DATE ____________ PERIOD _____
13-313-3
Reading to Learn MathematicsVolumes of Spheres
NAME ______________________________________________ DATE ____________ PERIOD _____
13-313-3
© Glencoe/McGraw-Hill 739 Glencoe Geometry
Less
on
13-
3
Pre-Activity How can you find the volume of Earth?
Read the introduction to Lesson 13-3 at the top of page 702 in your textbook.
How would you estimate the radius of Earth based on Eratosthenes’estimate of its diameter?
Reading the Lesson
1. Name all solids from the following list for which each volume formula can be used:prism, pyramid, cone, cylinder, sphere, hemisphere.
a. V � Bh b. V � �43��r3
c. V � �13�Bh d. V � �r2h
e. V � �13��r2h f. V � �
23��r3
2. Let r represent the radius and d represent the diameter of a sphere. Determine whethereach formula below can be used to find the volume of a sphere, a hemisphere, or neither.
a. V � �2�
3r3� b. V � �
16��d3
c. V � �13��r3 d. V � �
34��r3
e. V � ��1d2
3� f. V � �
43��r2h
3. Compare the volumes of these three solids. Then complete the sentence below.
Of the three solids shown above, the has the largest volume and the
has the smallest volume.
Helping You Remember
4. A good way to remember something is to explain it to someone else. Suppose that your classmate Loretta knows that the expressions �
43��r3 and 4�r2 are used in finding
measurements related to spheres, but can’t remember which one is used to find thesurface area of a sphere and which one is used to find the volume. How can you help herto remember which is which?
2r
r
rrr
© Glencoe/McGraw-Hill 740 Glencoe Geometry
Spheres and DensityThe density of a metal is a ratio of its mass to its volume. Forexample, the mass of aluminum is 2.7 grams per cubic centimeter.Here is a list of several metals and their densities.
Aluminum 2.7 g/cm3 Copper 8.96 g/cm3
Gold 19.32 g/cm3 Iron 7.874 g/cm3
Lead 11.35 g/cm3 Platinum 21.45 g/cm3
Silver 10.50 g/cm3
To calculate the mass of a piece of metal, multiply volume by density.
Find the mass of a silver ball that is 0.8 cm in diameter.
M � D V
� 10.5 �43��(0.4)3
� 10.5 (0.27)� 2.83
The mass is about 2.83 grams.
Find the mass of each metal ball described. Assume the balls are spherical. Round your answers to the nearest tenth.
1. a copper ball 1.2 cm in diameter
2. a gold ball 0.6 cm in diameter
3. an aluminum ball with radius 3 cm
4. a platinum ball with radius 0.7 cm
Solve. Assume the balls are spherical. Round your answers to the nearest tenth.
5. A lead ball weighs 326 g. Find the radius of the ball to the nearest tenth of a centimeter.
6. An iron ball weighs 804 g. Find the diameter of the ball to the nearest tenth of a centimeter.
7. A silver ball and a copper ball each have a diameter of 3.5 cm.Which weighs more? How much more?
8. An aluminum ball and a lead ball each have a radius of 1.2 cm.Which weighs more? How much more?
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
13-313-3
ExampleExample
Study Guide and InterventionCongruent and Similar Solids
NAME ______________________________________________ DATE ____________ PERIOD _____
13-413-4
© Glencoe/McGraw-Hill 741 Glencoe Geometry
Less
on
13-
4
Congruent or Similar Solids If the corresponding angles and sides of two solids arecongruent, then the solids are congruent. Also, the corresponding faces are congruent andtheir surface areas and volumes are equal. Solids that have the same shape but aredifferent sizes are similar. You can determine whether two solids are similar by comparingthe ratio, or scale factor, of corresponding linear measurements.
Describe each pair of solids.
• Figures I and II are similar because the figures have the same shape. The ratio of eachpair of corresponding sides is 1:3.
• Figures III and IV are congruent because they have the same shape and all correspondingmeasurements are the same.
• Figures V and VI are not congruent, and they are not similar because �48� �
1122�.
Determine whether each pair of solids are similar, congruent, or neither.
1. 2.
3. 4.
5. 6.2
7
21
6
5
8
5
8
4
4
88
5
5
2
2
2
26
6
7
7
12
4
5
1
106
8
53
4
I II III IV V VIsimilar congruent non-similar
12 5
5
5 12
12 4
85
5
5
7
7
9
6
4 32
ExercisesExercises
ExampleExample
© Glencoe/McGraw-Hill 742 Glencoe Geometry
Properties of Similar Solids These two solids are similar with a scale factor of 1:2. The surface areas are 62 cm2 and 248 cm2 and the volumes are 30 cm3 and 240 cm3. Notice that the ratio of the surface areas is 62:248, which is 1:4 or 12:22, and the ratio of the volumes is 30:240, which is 1:8 or 13:23.
If two solids are similar with a scale factor of a :b, then the surface areas have a ratio of a2:b2, and the volumes have a ratio of a3:b3.
Use the two spheres.a. Find the scale factor for the two spheres.
The scale factor for the two spheres is the same as the ratio of their radii, or 5:3.
b. Find the ratio of the surface areas of the two spheres.The ratio of the surface areas is 52:32 or 25:9.
c. Find the ratio of the volumes of the two spheres.The ratio of the volumes is 53:33 or 125:27.
Find the scale factor for each pair of similar figures. Then find the ratio of theirsurface areas and the ratio of their volumes.
1. 2.
3. 4.
5. 6.
8 6
5
3
1215
4 yd16 yd
15 m12 m
7 in. 4 in.
3 ft4 ft
5 cm3 cm
10 cm5 cm2 cm
3 cm
6 cm
4 cm
Study Guide and Intervention (continued)
Congruent and Similar Solids
NAME ______________________________________________ DATE ____________ PERIOD _____
13-413-4
ExercisesExercises
ExampleExample
Skills PracticeCongruent and Similar Solids
NAME ______________________________________________ DATE ____________ PERIOD _____
13-413-4
© Glencoe/McGraw-Hill 743 Glencoe Geometry
Less
on
13-
4
Determine whether each pair of solids are similar, congruent, or neither.
1.
2.
3.
4.
For Exercises 5–8, refer to the two similar prisms.
5. Find the scale factor of the two prisms.
6. Find the ratio of the surface areas.
7. Find the ratio of the volumes.
8. Suppose the volume of the larger prism is 810 cubic centimeters. Find the volume of thesmaller prism.
15 cm12 cm
9 cm 10 cm8 cm
6 cm
18 in.
16 in.16 in.
9 in.
6 mm
6 mm
4 mm9 mm
12 ft12 ft
14 ft
20 ft20 ft
21 ft
20 cm20 cm
10 cm
4 cm40 cm
8 cm
© Glencoe/McGraw-Hill 744 Glencoe Geometry
Determine whether each pair of solids are similar, congruent, or neither.
1.
2.
3.
4.
For Exercises 5–8, refer to the two similar prisms.
5. Find the scale factor of the two prisms.
6. Find the ratio of the surface areas.
7. Find the ratio of the volumes.
8. Suppose the surface area of the larger prism is 2560 square meters. Find the surfacearea of the smaller prism.
9. MINIATURES Frank Lloyd Wright designed every aspect of the Imperial Hotel in Tokyo,including the chairs. The dimensions of a miniature Imperial Hotel chair are 6.25 inches �3 inches � 2.5 inches. If the scale of the replica is 1:6, what are the dimensions of theoriginal chair?
20 m
20 m
22 m
12 m
12 m
13.2 m
7.5 cm
20 cm
15 cm
4.5 cm
12 cm9 cm
18 ft24 ft
24 ft9 ft
12 m
12 m15 m
2.5 m
2 m9.6 m
25 in.
15 in.
30 in.20 in.
Practice Congruent and Similar Solids
NAME ______________________________________________ DATE ____________ PERIOD _____
13-413-4
Reading to Learn MathematicsCongruent and Similar Solids
NAME ______________________________________________ DATE ____________ PERIOD _____
13-413-4
© Glencoe/McGraw-Hill 745 Glencoe Geometry
Less
on
13-
4
Pre-Activity How are similar solids applied to miniature collectibles?
Read the introduction to Lesson 13-4 at the top of page 707 in your textbook.
If you want to make a miniature with a scale factor of 1:64, how can youuse the actual object to find the measurements you should use to constructthe miniature?
Reading the Lesson1. Determine whether each statement is always, sometimes, or never true.
a. Two cubes are similar.b. Two cones are similar.c. Two cylinders in which the height is twice the diameter are similar.d. Two cylinders with the same volume are congruent.e. A prism with a square base and a square pyramid are similar.f. Two rectangular prisms with equal surface areas are similar.g. Nonsimilar solids have different volumes.h. Two hemispheres with the same radius are congruent.
2. Supply the missing ratios.
a. If the ratio of the diameters of two spheres is 3:1, then the ratio of their surface areas
is , and the ratio of their volumes is .
b. If the ratio of the radii of two hemispheres is 2:5, then the ratio of their surface areas
is , and the ratio of their volumes is .
c. If two cones are similar and the ratio of their heights is �43�, then the ratio of their
volumes is , and the ratio of their surface areas is .
d. If two cylinders are similar and the ratio of their surface areas is 100:49, then the
ratio of the radii of their bases is , and the ratio of their volumes is
.
Helping You Remember3. A good way to remember a new mathematical concept is to relate it to something you
already know. How can what you know about the units used to measure lengths, areas,and volumes help you to remember the theorem about the ratios of surface areas andvolumes of similar solids?
© Glencoe/McGraw-Hill 746 Glencoe Geometry
Congruent and Similar Solids
Determine whether each pair of solids is similar, congruent, or neither.
1. 2.
3. 4.
The two rectangular prisms shown at the right are similar.
5. Find the ratio of the perimeters of the bases.
6. What is the ratio of the surface areas?
7. Suppose the volume of the smaller prism is 60 in3.Find the volume of the larger prism.
Determine whether each statement is true or false. If the statement is false, rewrite it so that it is true.
8. If two cylinders are similar, then their volumes are equal.
9. Doubling the height of a cylinder doubles the volume.
10. Two solids are congruent if they have the same shape.
7 in.5 in.
24 yd
12 yd
12 yd6 yd
8 yd
16 yd12 m
3 m
3 m
3 m
3 m
3 m3 m
4 m
4 m4 m 4 m
4 m
10 m
48 m
16 m
15 m
14 cm
11 cm
7 cm
7 cm
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
13-413-4
Study Guide and InterventionCoordinates in Space
NAME ______________________________________________ DATE ____________ PERIOD _____
13-513-5
© Glencoe/McGraw-Hill 747 Glencoe Geometry
Less
on
13-
5
Graph Solids in Space In space, you can describe the location of a point using an ordered triple of realnumbers. The x-, y-, and z-axes are perpendicular to each other, and the coordinates for point P are the ordered triple (�4, 6, 5). A rectangular prism can bedrawn to show perspective.
Graph the rectangular solid that contains the ordered triple (2, 1, �2) and the origin. Label the coordinates of each vertex.• Plot the x-coordinate first. Draw a solid segment
from the origin 2 units in the positive direction.• Plot the y-coordinate next. Draw a solid segment
1 unit in the positive direction.• Plot the z-coordinate next. Draw a solid segment
2 units in the negative direction.• Draw the rectangular prism, using dotted lines for
hidden edges of the prism.• Label the coordinates of each vertex.
Graph the rectangular solid that contains the given point and the origin asvertices. Label the coordinates of each vertex.
1. A(2, 1, 3) 2. G(�1, 2, 3)
3. P(�2, 1, �1) 4. T(�1, 3, 2)
y
x
z
(0, 0, 0)
(0, 3, 0)
(�1, 3, 0)
(0, 0, 2) (0, 3, 2)
(�1, 0, 2)
(�1, 0, 0)
T (�1, 3, 2)
y
x
z
(0, 0, 0)
(0, 1, 0)
P(�2, 1, �1)
(�2, 0, �1) (�2, 1, 0)(�2, 0, 0)
(0, 0, �1) (0, 1, �1)
y
x
z
(0, 0, 0)
(0, 0, 3)
(�1, 2, 0)(�1, 0, 0)
(�1, 0, 3)G(�1, 2, 3)
(0, 2, 0)
(0, 2, 3)
y
x
z(0, 0, 3)
(0, 0, 0)
(2, 0, 3)
(2, 0, 0)(2, 1, 0)
(0, 1, 0)
(0, 1, 3)
A(2, 1, 3)
y
x
z
(0, 0, 0) (0, 1, 0)
(0, 1, �2)
(2, 1, �2)(2, 0, �2)
(0, 0, �2)
(2, 0, 0) (2, 1, 0)
y
x
z
O
P(�4, 6, 5)
ExercisesExercises
ExampleExample
© Glencoe/McGraw-Hill 748 Glencoe Geometry
Distance and Midpoint Formulas You can extend the Distance Formula and theMidpoint Formula to three dimensions to find the distance between two points in space and to find the midpoint of the segment connecting two points.
Distance Formula Given two points A(x1, y1, z1) and B(x2, y2, z2) in space, the distance between
in Space A and B is given by AB � �(x1 ��x2)2 �� (y1 �� y2)2 �� (z1 �� z2)2�.
Midpoint Formula Given two points A(x1, y1, z1) and B(x2, y2, z2) in space, the midpoint of A�B� is
in Space at ��x1 �
2x2�, �
y1 �
2y2�, �
z1 �
2z2��.
Determine the distance between A(3, 2, �5) and B(�4, 6, 9).Then determine the coordinates of the midpoint of A�B�.
AB � �(x1 ��x2)2 �� ( y1 �� y2)2 �� (z1 �� z2)2�� �(3 � (��4))2�� (2 �� 6)2 �� (�5 �� 9)2�� �72 � (��4)2 �� (�14�)2�� �49 ��16 ��196�� 16.2
midpoint of A�B� � ��x1 �
2x2�, �
y1 �
2y2�, �
z1 �
2z2��
� ��3 �
2(�4)�, �
2 �2
6�, ��5
2� 9��
� (�0.5, 4, 2)
Determine the distance between each pair of points. Then determine thecoordinates of the midpoint M of the segment joining the pair of points.
1. A(0, 7, �4) and B(�2, 8, 3) 2. C(�7, 6, 5) and D(10, 2, �5)
3. E(3, 1, �2) and F(�2, 3, 4) 4. G(�4, 1, 1) and H(0, 2, �1)
5. J(6, 1, �2) and K(�1, �2, 1) 6. L(�5, 0, �3) and N(0, 0, �4)
Study Guide and Intervention (continued)
Coordinates in Space
NAME ______________________________________________ DATE ____________ PERIOD _____
13-513-5
ExercisesExercises
ExampleExample
Skills PracticeCoordinates in Space
NAME ______________________________________________ DATE ____________ PERIOD _____
13-513-5
© Glencoe/McGraw-Hill 749 Glencoe Geometry
Less
on
13-
5
Graph the rectangular solid that contains the given point and the origin asvertices. Label the coordinates of each vertex.
1. A(�5, 3, 2) 2. H(3, 2, 5)
3. Dilate the prism by a scale factor of 2. Graph the image under the dilation.
Determine the distance between each pair of points. Then determine thecoordinates of the midpoint M of the segment joining the pair of points.
4. R(2, 1, 0) and S(3, 3, 4) 5. Q(5, 0, �2) and T(2, 3, 2)
6. A(�4, 1, 6) and B(�1, 0, 4) 7. J(0, 5, 1) and K(4, �3, 2)
A�B�
C� D�E�F�
G�H�
y
x
z
AB
C
G H
ED
F
N(0, 0, 0)
M(3, 0, 0)L(3, 2, 0)
P(0, 2, 0)
K(0, 2, 5)J(0, 0, 5)
I(3, 0, 5)
H(3, 2, 5)
A(�5, 3, 2)
E(�5, 3, 0)
B(�5, 0, 2)
C(0, 0, 2)D(0, 3, 2)
H(0, 3, 0)
G(0, 0, 0)
F (�5, 0, 0)
© Glencoe/McGraw-Hill 750 Glencoe Geometry
Graph the rectangular solid that contains the given point and the origin asvertices. Label the coordinates of each vertex.
1. E(4, 6, �2) 2. R(�3, �5, 4)
Determine the distance between each pair of points. Then determine thecoordinates of the midpoint M of the segment joining the pair of points.
3. Y(�5, 1, 2) and Z(3, �3, 1) 4. E(4, 2, 0) and F(3, 2, �2)
5. B(�2, �2, �3) and C(1, �3, 0) 6. H(2, 0, �3) and I(4, �1, 5)
7. ANIMATION Derek wants to animate an image for his science presentation by movingit from one position to another. The mesh of the image is a rectangular prism withcoordinates A(�3, 2, 3), B(�3, 0, 3), C(0, 0, 3), D(0, 2, 3), E(�3, 2, 0), F(�3, 0, 0), G(0, 0, 0),and H(0, 2, 0). Find the coordinates of the mesh after the translation (x, y, z) → (x � 7, y, z).Graph both the preimage and image of the mesh.
A�B�
C� D�
E�
F�
G� H�
AB
C D EFG
H
X(0, 0, 0)
Y(0, �5, 0)
V(�3, �5, 0)
R(�3, �5, 4) S(�3, 0, 4)
T(0, 0, 4)U(0, �5, 4)
W(�3, 0, 0)
K(0, 0, 0)
J(4, 0, 0)I(4, 6, 0)
L(0, 6, 0)
H(0, 6, �2)
E(4, 6, �2)F(4, 0, �2)
G(0, 0, �2)
Practice Coordinates in Space
NAME ______________________________________________ DATE ____________ PERIOD _____
13-513-5
Reading to Learn MathematicsCoordinates in Space
NAME ______________________________________________ DATE ____________ PERIOD _____
13-513-5
© Glencoe/McGraw-Hill 751 Glencoe Geometry
Less
on
13-
5
Pre-Activity How is three-dimensional graphing used in computer animation?
Read the introduction to Lesson 13-5 at the top of page 714 in your textbook.
Why would a mesh be created first?
Reading the Lesson
1. Refer to the figure. Match each point from the first column with its coordinates from the second column.
a. A i. (3, 0, 0)
b. B ii. (3, 0, �4)
c. O iii. (3, �2, 0)
d. J iv. (3, �2, �4)
e. H v. (0, 0, 0)
f. K vi. (0, �2, 0)
g. T vii. (0, �2, �4)
h. R viii. (0, 0, �4)
2. Which of the following expressions give the distance between the points at (4, �1, �5)and (�3, 2, �9)?
A. �72 � (��3)2 �� 42� B. �12 � 1�2 � (��14)2�
C. �22 � 2�2 � 42� D. ��12�, �
12�, �7�
E. �(�3 �� 4)2 �� (�1 �� 2)2 �� (�9 �� 5)2� F. �24�
G. �(�3 �� 4)2 �� [2 ��(�1)]2� � [��9 � (��5)]2� H. �74�
Helping You Remember
3. A good way to remember new mathematical formulas is to relate them to ones youalready know. How can you use your knowledge of the Distance and Midpoint Formulasin two dimensions to remember the formulas in three dimensions?
y
x
z
A
K
BO
R
H
T
J
© Glencoe/McGraw-Hill 752 Glencoe Geometry
Planes and Cylindrical SurfacesConsider the points (x, y, z) in space whose coordinates satisfy the equation z � 1. Since x and y do not occur in the equation, any point with its z-coordinate equal to 1 has coordinates that satisfy the equation. These are the points in the plane 1 unit above the xy-plane. This plane is perpendicular to the z-axis at (0, 0, 1).
Next consider the points (x, y, z) whose coordinates satisfy x2 � y2 � 16. In the xy-plane,all points on the circle with center (0, 0, 0) andradius 4 have coordinates that satisfy the equation. In the plane perpendicular to the z-axis at (0, 0, k), the points that satisfy theequation are those on the circle with center (0, 0, k) and radius 4. The graph in space of x2 � y2 � 16 is an infinite cylindrical surface whose axis is the z-axis and whose radius is 4.
Describe the graph in space of each equation. You may find it helpful to make sketches on a separate sheet.
1. x � 5
2. y � �2
3. x � y � 7
4. z2 � y2 � 25
5. (x � 2)2 � (y � 5)2 � 1
6. x2 � y2 � z2 � 0
z
y
x
O
(0, 0, k)
plane for z � k
z
y
x
O
(0, 0, 1)N
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
13-513-5
Chapter 13 Test, Form 11313
© Glencoe/McGraw-Hill 753 Glencoe Geometry
Ass
essm
entsWrite the letter for the correct answer in the blank at the right of each
question.
1. Which of the following could be the units of measure for the volume of a solid?A. cubic inches B. square inches C. inches D. cubic seconds
2. The area of the base of a prism is 96 square centimeters and the height is 9 centimeters. Find the volume.A. 288 cm3 B. 864 cm3 C. 932 cm3 D. 7776 cm3
3. The volume of a cylinder is 62.8 cubic meters and the radius is 2 meters. Findthe height to the nearest meter.A. 20 m B. 10 m C. 8 m D. 5 m
4. A cylinder has a radius that is 4 inches long and a height that is 9 inches long.Find the volume to the nearest tenth.A. 131.1 in3 B. 226.2 in3 C. 452.4 in3 D. 1809.6 in3
5. Find the volume of a pyramid with a height of 10 inches and a base with anarea of 21 square inches.A. 210 in3 B. 105 in3 C. 70 in3 D. 35 in3
6. Find the volume of the pyramid.A. 360 cm3 B. 390 cm3
C. 1080 cm3 D. 1170 cm3
7. A cone and a cylinder have the same radius and the same height. The volumeof the cone is what fraction of the volume of the cylinder?
A. �12� B. �
13� C. �
14� D. �
18�
8. Find the volume to the nearest tenth.A. 1206.4 in3 B. 402.1 in3
C. 301.6 in3 D. 100.5 in3
9. A sphere has a radius that is 12 centimeters long. Find the volume to thenearest tenth.A. 7238.2 cm3 B. 3619.1 cm3 C. 1809.6 cm3 D. 603.2 cm3
10. A sphere has a volume that is 36� cubic meters. Find the radius of the sphere.A. 2 m B. 3 m C. 6 m D. 12 m
11. The radius of a sphere is increased from 6 inches to 8 inches. How much isthe volume increased to the nearest tenth?A. 3719.6 in3 B. 1239.9 in3 C. 117.3 in3 D. 33.5 in3
6 in.
10 in.
10 cm9 cm
13 cm
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 754 Glencoe Geometry
Chapter 13 Test, Form 1 (continued)1313
12.
13.
14.
15.
16.
17.
18.
19.
20.
12. Which solid has the greater volume?A. sphere B. cylinderC. The volumes D. not enough
are equal. information
13. Which solid is similar to this solid?A. B.
C. D.
14. Which of the following describes the two spheres?A. congruent B. similarC. both A and B D. neither A nor B
15. The ratio of the side lengths of two cubes is 3:7. Find the ratio of their volumes.A. 3:7 B. 9:21 C. 9:49 D. 27:343
16. Two similar prisms have equilateral triangular bases and the edges of thebases are 50 centimeters and 20 centimeters. Find the ratio of the perimetersof the bases.A. 5�2�:2�5� B. 5:2 C. 25:4 D. 125:8
17. Find the coordinates of the image of A(�3, 5, 6) under the translation (x, y, z) → (x � 3, y � 5, z � 1).A. A�(0, 0, 5) B. A�(0, 10, 5) C. A�(�6, 0, �7) D. A�(�6, 10, 5)
18. The graph of the rectangular solid contains the origin and which other point?A. (3, 2, 4) B. (2, 4, 3)C. (4, 3, 2) D. (3, 4, 2)
For Questions 19 and 20, A(6, 5, 4) and B(�2, 4, 0).
19. Find the coordinates of the midpoint of A�B�.
A. �4, �12�, 2� B. (8, 1, 4) C. (4, 9, 4) D. �2, �
92�, 2�
20. Find the distance between A and B.A. �13� B. �17� C. 9 D. �113�
Bonus Describe the solid that could be formed by rotating this figure about line �. 3 cm
6 cm
�
y
x
z
9 ft 6 ft
15 in.
18 in.
15 in.15 in.
18 in.
12 in.
10 in.
10 in.18 in.
5 in.6 in.
3r
r
r
B:
NAME DATE PERIOD
Chapter 13 Test, Form 2A1313
© Glencoe/McGraw-Hill 755 Glencoe Geometry
Ass
essm
entsWrite the letter for the correct answer in the blank at the right of each
question.
1. How many cubic feet are in one cubic yard?A. 3 B. 9 C. 27 D. 81
2. The surface area of a cube is 96 square feet. Find the volume.A. 4 ft3 B. 16 ft3 C. 64 ft3 D. 256 ft3
3. A cylinder whose height is 5 meters has a volume of 320� cubic meters. Findthe radius of the cylinder.A. 8 m B. 12.8 m C. 64 m D. 201 m
4. A cylinder has a 10-inch diameter and an 11-inch height. Find the volume tothe nearest tenth.A. 172.8 in3 B. 345.6 in3 C. 863.9 in3 D. 3455.8 in3
5. A square pyramid has a height that is 8 centimeters long and a base withsides that are each 9 centimeters long. Find the volume.A. 648 cm3 B. 324 cm3 C. 216 cm3 D. 162 cm3
6. Find the volume to the nearest tenth.A. 80.0 ft3 B. 78.4 ft3
C. 48.0 ft3 D. 39.2 ft3
7. The volume of a cone is 1080� cubic centimeters and the radius is 18centimeters. Find the height.A. 5 cm B. 10 cm C. 20 cm D. 30 cm
8. Find the volume to the nearest tenth.A. 3619.1 m3 B. 4825.5 m3
C. 14,476.5 m3 D. 43,429.4 m3
9. A sphere has a 21-inch radius. Find the volume to the nearest tenth.A. 38,792.4 in3 B. 19,396.2 in3 C. 5541.8 in3 D. 1847.3 in3
10. A sphere has a volume that is 972� cubic inches. Find the radius.A. 2 in. B. 3 in. C. 6 in. D. 9 in.
11. A sphere has a 6-inch radius. A cone has a 12-inch height and base with a 6-inch radius. Compare their volumes.A. The volume of the sphere is greater.B. The volume of the cone is greater.C. The volumes are equal.D. not enough information
60�24 m
10 ft
10 ft6 ft
4 ft
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NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 756 Glencoe Geometry
Chapter 13 Test, Form 2A (continued)1313
12.
13.
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15.
16.
17.
18.
19.
20.
12. A golf ball has a 3.8-centimeter diameter and a tennis ball has a 7-centimeterdiameter. Find the difference between their volumes to the nearest tenth.A. 1206.9 cm3 B. 220.5 cm3 C. 150.9 cm3 D. 17.2 cm3
13. Two solids are congruent. Which statement about the two solids is true?A. They have a scale factor of 1.B. Their corresponding angles are congruent.C. The ratio of the corresponding linear measurements is 1:1.D. All of the above are true statements.
14. Two square pyramids are similar. The sides of the bases are 4 inches and 12 inches. The height of the smaller pyramid is 6 inches. Find the height ofthe larger pyramid.A. 24 in. B. 18 in. C. 16 in. D. 14 in.
15. The ratio of the radii of two similar cylinders is 3:5. The volume of the smallercylinder is 54� cubic centimeters. Find the volume of the larger cylinder.A. 90� cm3 B. 150� cm3 C. 250� cm3 D. 540� cm3
16. The ratio of the heights of two similar solids is 7:9. Find the ratio of theirvolumes.A. 7:9 B. 14:18 C. 49:81 D. 343:729
17. The graph of the rectangular solid contains the origin and which other point?A. (5, 2, 3) B. (2, 3, 5)C. (5, 3, 2) D. (2, 5, 3)
18. Find the coordinates of B(�9, 6, 12) under a dilation of factor �23�.
A. B����227�, 9, 18� B. B����
235�, �
230�, �
338��
C. B�(�3, 2, 4) D. B�(�6, 4, 8)
For Questions 19 and 20, C(4, 3, 2) and D(5, �1, �2).
19. Find the coordinates of the midpoint of C�D�.
A. ���12�, 2, 2� B. (�1, 4, 4) C. (9, 2, 0) D. ��
92�, 1, 0�
20. Find the distance between C and D.A. �85� B. �33� C. �11� D. �7�
Bonus A cone is formed by rolling up a 90° sector of a circle having an 8-inch radius. Find the volume of the cone to the nearest tenth.
8 in.8 in.
y
x
z
B:
NAME DATE PERIOD
Chapter 13 Test, Form 2B1313
© Glencoe/McGraw-Hill 757 Glencoe Geometry
Ass
essm
entsWrite the letter for the correct answer in the blank at the right of each
question.
1. Which of the following is the formula for the volume of a prism?A. V � 2�r2 � 2�rh B. V � phC. V � �r2 D. V � Bh
2. The lateral area of a cube is 324 square centimeters. Find the volume.A. 9 cm3 B. 81 cm3 C. 729 cm3 D. 972 cm3
3. Find the volume to the nearest tenth.A. 31.4 in3 B. 41.9 in3
C. 125.7 in3 D. 502.7 in3
4. A cylinder has a radius that is 7 inches long and a height that is 10 incheslong. Find the volume to the nearest tenth.A. 1539.4 in3 B. 490.0 in3 C. 219.9 in3 D. 70.0 in3
5. A right triangular pyramid has a 12-meter height and a base with legs thatare 3 meters and 4 meters long. Find the volume.A. 144 m3 B. 72 m3 C. 48 m3 D. 24 m3
6. The volume of a square pyramid is 100 cubic feet and the height is 10 feetlong. Find the length of a side of the base.A. 15 ft B. �30� ft C. 7.5 ft D. �5� ft
7. The volume of a cone is 336� cubic feet and the height is 7 feet long. Find theradius.A. 144 ft B. 36 ft C. 24 ft D. 12 ft
8. Find the volume to the nearest tenth.A. 41,224.0 m3 B. 20,612.0 m3
C. 10,306.0 m3 D. 763.4 m3
9. A sphere has a 48-centimeter diameter. Find the volume to the nearest tenth.A. 463,246.7 cm3 B. 57,905.8 cm3 C. 28,952.9 cm3 D. 7238.2 cm3
10. A sphere has a volume that is 288� cubic inches. Find the radius.A. 3 in. B. 6 in. C. 8 in. D. 12 in.
11. A sphere has a 10-centimeter radius and a cone has a 15-centimeter heightand a base with an 8-centimeter radius. Compare their volumes.A. The volume of the sphere is greater.B. The volume of the cone is greater.C. Their volumes are equal.D. not enough information
45�27 m
10 in.
4 in.
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NAME DATE PERIOD
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© Glencoe/McGraw-Hill 758 Glencoe Geometry
Chapter 13 Test, Form 2B (continued)1313
12.
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15.
16.
17.
18.
19.
20.
12. A beach ball has an 18-inch diameter and a kick ball has a 12-inch diameter.Find the difference of the volumes to the nearest tenth.A. 17,190.8 in3 B. 2148.8 in3 C. 188.5 in3 D. 113.1 in3
13. Two solids with the same shape but not necessarily the same size are .A. similar solidsB. congruent solidsC. congruent and similar solidsD. neither congruent nor similar solids
14. Find the scale factor between the two similar cones.A. 3:8 B. 1:3C. 1:2 D. 1:4
15. The ratio of the heights of two similar solids is 6:11. Find the ratio of theirsurface areas.A. 6:11 B. 36:121 C. 216:1331 D. 24:44
16. The ratio of the radii of two spheres is 7:3. The volume of the larger sphere is343� cubic feet. Find the volume of the smaller sphere.A. 147� ft3 B. 63� ft3 C. 36� ft3 D. 27� ft3
17. The graph of the rectangular solid contains the origin and which other point?A. (6, 1, 2) B. (1, 2, 6)C. (1, 6, 2) D. (2, 6, 1)
18. Find the image of C(�10, �6, 5) under the translation (x, y, z) → (x � 5, y � 8, z � 4).A. C�(�15, 2, 1) B. C�(�5, �14, 9)C. C�(�5, �14, �1) D. C�(50, �48, �20)
For Questions 19 and 20, E(8, �7, 6) and F(10, �8, 4).19. Find the distance between E and F.
A. �649� B. �13� C. 3 D. 1
20. Find the coordinates of the midpoint of EF.
A. �9, ��125�, 5� B. (18, �5, 10) C. ��1, �
12�, 1� D. (�2, 1, 2)
Bonus Find the volume of plastic needed to mold this tube to the nearest tenth.
2 cm
13 cm
1 cm
y
x
z
6 ft
16 ft8 ft
3 ft
?
B:
NAME DATE PERIOD
Chapter 13 Test, Form 2C1313
© Glencoe/McGraw-Hill 759 Glencoe Geometry
Ass
essm
ents1. A box has a length of 12 inches, a width of 9 inches, and a
height of 4 inches. Find the volume.
2. The volume of a rectangular prism is 120 cubic feet and thearea of the base is 60 square feet. Find the length of a lateraledge of the prism.
3. A cylinder has a 12-foot radius and a 17-foot height. Find thevolume to the nearest tenth.
4. Find the volume to the nearest tenth.
5. A regular hexagonal pyramid has a height that is 15 feet and a base 6 feet on each side. Find the volume.
6. The volume of a pyramid is 120 cubic inches and the area ofthe base is 50 square inches. Find the height.
7. The height of a cone is doubled and the radius is tripled. Howmany times greater is the volume?
8. Find the volume to the nearest tenth.
9. A sphere has a diameter that is 7.36 inches long. Find thevolume to the nearest tenth.
10. The surface area of a sphere is 804.2 square inches. Find thevolume to the nearest cubic inch.
11. A sphere is circumscribed about an 8-inch by 8-inch by 8-inchcube. Find the volume of the sphere to the nearest cubic inch.
12. Find the volume to the nearest tenth.
9 cm5 cm
30�
8 ft 5 ft
20 m
6 m
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NAME DATE PERIOD
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© Glencoe/McGraw-Hill 760 Glencoe Geometry
Chapter 13 Test, Form 2C (continued)1313
13. Determine whether the statement Two cubes are similar isalways, sometimes, or never true.
14. Determine whether these two cylinders are congruent, similar,or neither.
15. The ratio of the heights of two similar prisms is 2:7. Thesurface area of the smaller prism is 50 square meters. Findthe surface area of the larger prism.
16. The ratio of the volumes of two similar solids is 8:27. Find theratio of their surface areas.
17. Find the image of D(11, �2, �9) under the translation (x, y, z) → (x � 4, y � 3, z � 6).
18. Graph the rectangular solid that contains the origin and thepoint A(1, 2, 3) as vertices.
For Questions 19 and 20, use a sphere that has a diameterwith endpoints X(�3, 4, 6) and Y(5, 6, 8).
19. Find the coordinates of the center of the sphere.
20. Find the radius of the sphere.
Bonus Find the volume of the solid formed by the rotation of�ABC about line m to the nearest tenth.
5 in.
AC
B13 in.
m
4 in.
10 in. 9 in.
3 in.
13.
14.
15.
16.
17.
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19.
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B:
y
x
z
A
NAME DATE PERIOD
Chapter 13 Test, Form 2D1313
© Glencoe/McGraw-Hill 761 Glencoe Geometry
Ass
essm
ents1. Find the volume.
2. An aquarium is 18 inches long, 8 inches wide, and 14 incheshigh. The water in it is 4 inches deep. Find the volume of the water.
3. Find the volume to the nearest tenth.
4. A cylindrical can has a volume of 72� cubic centimeters and aheight that is 8 centimeters. Find the radius.
5. A square pyramid has a height that is 51 inches and a basewith sides that are each 11 inches long. Find the volume.
6. The volume of a pyramid is 216 cubic inches and the height is18 inches. Find the area of the base.
7. The height of a cone is tripled and the radius is doubled. Thevolume is how many times as great?
8. Find the volume of the solid to the nearest tenth.
9. A sphere has a radius that is 2.94 centimeters long. Find thevolume to the nearest tenth.
10. The surface area of a sphere is 1809.6 square feet. Find thevolume to the nearest cubic foot.
11. A box has a 6-inch length, a 6-inch width, and a 6-inch height.Find the volume of the largest ball that will fit in this box tothe nearest tenth.
4 cm
6 cm
25 cm7 cm
6 cm
5 cm
5 cm
12 cm
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NAME DATE PERIOD
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© Glencoe/McGraw-Hill 762 Glencoe Geometry
Chapter 13 Test, Form 2D (continued)1313
12. Find the volume to the nearest tenth.
13. Determine whether the statement Two congruent solids haveequal volumes is always, sometimes, or never true.
14. Determine whether these cubes are congruent, similar,or neither.
15. The ratio of the heights of two similar pyramids is 2:5 and thevolume of the smaller pyramid is 100 cubic feet. Find thevolume of the larger pyramid.
16. The ratio of the surface areas of two similar solids is 64:81.Find the ratio of their volumes.
17. Find the image of X(�7, 2, 5) under a dilation with scale factor 4.
18. Graph the rectangular solid that contains the origin and thepoint A(2, 4, 6) as vertices.
For Questions 19 and 20, use a sphere that has a diameterwith endpoints A(�5, 4, 10) and B(�11, 8, �2).
19. Find the length of a diameter of the sphere.
20. Find the coordinates of the center of the sphere.
Bonus Find the coordinates of the point that is three fourths ofthe way from A(�11, 9, 2) to B(4, 4, �8).
6 cm 8 cm
11 in. 1 in.
12.
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15.
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19.
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B:
y
x
z
A
NAME DATE PERIOD
Chapter 13 Test, Form 31313
© Glencoe/McGraw-Hill 763 Glencoe Geometry
Ass
essm
ents1. Find the volume of a cube with a 5-meter edge.
2. Find the volume.
3. Find the volume.
4. The volume of a cylinder is 96� cubic meters and the height is6 meters. Find the length of the diameter of this cylinder.
5. Sam is filling a rectangular pan with liquid from a cylindricalcan. The can is three-fourths full of water. Determine whetherall of the water will fit in the pan. Explain.
For Questions 6–10, find the volume to the nearest tenth.
6. The height of a regular octagonal pyramid is 12 centimetersand the apothem of the base is 4 centimeters.
7. 8.
9. 10.
11. A hemisphere has a radius that is 33 centimeters long. Findthe volume to the nearest tenth.
2 cm 8 cm
15 cm6 in.
3 in.
5 in.
2 in. 8 in.
13 in.
6 cm6 cm
6 cm
6 cm
8 in.6 in.
7 in.3 in.2 in.
2 in.
19 in.
3 cm2 cm
8 cm
10 cm
12 cm
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NAME DATE PERIOD
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© Glencoe/McGraw-Hill 764 Glencoe Geometry
Chapter 13 Test, Form 3 (continued)1313
12. The radius of a sphere is multiplied by 4. How many timesgreater is the volume?
13. A cone is 9 centimeters deep and 4 centimeters across the top. Asingle scoop of ice cream, 4 centimeters in diameter, is placed ontop of the cone. If the ice cream melts into the cone, determinewhether the melted ice cream will fit in the cone. Explain.
14. Determine whether these two pyramids are congruent, similar, or neither.
15. The ratio of the volumes of two similar solids is 1:2. Find theratio of their surface areas.
16. The volumes of two spheres are in the ratio of 8:27. The radiusof the smaller sphere is 30 inches. Find the radius of thelarger sphere.
17. Dilate the cube by a factor of �12�. Then graph the image under
the dilation.
18. The center of a sphere is at A(5, �2, 8) and one endpoint of adiameter is at B(7, 5, 6). Find the coordinates of C, the otherendpoint of the diameter.
19. Find the distance between A(2�3�, �2, �2�) and B(3�3�, 1, 2�2�).
20. An airplane at an elevation of 1 mile is 20 miles east and 70 miles south of an airport. A second airplane at an elevation of
�12� mile is 50 miles west and 25 miles north of the airport. Find
the distance between the two airplanes to the nearest tenth.
Bonus A molding machine produces 4-centimeter cubes of plastic.The volume of molten plastic needed to produce these cubesis 11% more than the volume of plastic in the solid cubes.Find the amount of molten plastic needed to produce 100 cubes. (Note: 1 milliliter � 1 cubic centimeter.)
5 m
5 m
8 m
4 m
5 m
8 m6.4 m
8 m
12.
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B:
y
x
z
NAME DATE PERIOD
Chapter 13 Open-Ended Assessment1313
© Glencoe/McGraw-Hill 765 Glencoe Geometry
Ass
essm
entsDemonstrate your knowledge by giving a clear, concise solution to
each problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solution in more than one way orinvestigate beyond the requirements of the problem.
1. Graph a rectangular prism and its image under a dilation with scale
factor �14�. Write the coordinates of the vertices of your original prism and
those of the image.
2. Write a formula for the volume of this solid in terms of the radius r.Explain how you determined your answer.
3. Give the dimensions of two cylinders in which the first has a greater volumethan the second, but the second has greater surface area than the first.
4. Draw and label the dimensions of a prism and a pyramid that have thesame volume.
5. Demonstrate how the formula for the volume of a cylinder can be obtainedfrom the formula for the volume of a prism.
6. Find one set of coordinates for A and C so that their midpoint is B(3, 4, 5).
45�
2r
r
r
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 766 Glencoe Geometry
Chapter 13 Vocabulary Test/Review1313
Determine whether each sentence is true or false. If false,replace the underlined word or formula to make a truesentence.
1. Congruent solids have the same shape but not the same size.
2. Similar solids have the same shape and the same size.
3. An ordered pair gives the coordinates of a point in space.
4. Volume is the measure of the amount of space that a figureencloses.
5. V � �r2h is the formula for the volume of a cone.
6. V � 4�r2 is the formula for the volume of a sphere.
7. V � Bh is the formula for the volume of a prism.
8. V � �13�Bh is the formula for the volume of a pyramid.
9. V � ��r
3
2h� is the formula for the volume of a cylinder.
10. The formula for the distance between two points in space is
d � �(x1 ��x2)2 �� ( y1 �� y2)2 �� (z1 �� z2)2�.
In your own words—
11. Explain how to find the ratio of the volume of two similar solidsif a:b is the ratio of the lengths of the corresponding edges.
12. Explain how to find the midpoint of (x1, y1, z1) and (x2, y2, z2).
1.
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congruent solids ordered triple similar solids volume
NAME DATE PERIOD
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Chapter 13 Quiz (Lessons 13–1 and 13–2)
1313
© Glencoe/McGraw-Hill 767 Glencoe Geometry
Ass
essm
ents
NAME DATE PERIOD
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1.
2.
3.
4.
5.
1. A rectangular prism has a length of 16 feet, a width of 9 feet,and height of 8 feet. Find the volume.
2. The volume of a rectangular prism is 198 cubic centimeters,the length is 11 centimeters, and the height is 9 centimeters.Find the width.
3. A cylinder has a diameter of 20 inches and height of 9 inches.Find the volume to the nearest tenth.
4. A pyramid has a height of 18 centimeters and a base with anarea of 26 square centimeters. Find the volume.
5. Find the volume to the nearest tenth. 16 cm
17 cm
Chapter 13 Quiz (Lesson 13–3)
1313
1.
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4.
5.
1. The radius of a sphere is doubled. How many times greater isits volume?
2. A hemisphere has a base with an area that is 25� squarecentimeters. Find the volume to the nearest tenth.
3. A sphere is inscribed in a cube whose volume is 1728 cubicmillimeters. Find the volume of the sphere to the nearest tenth.
4. Find the volume to the nearest tenth.
5. STANDARDIZED TEST PRACTICE A sphere has a radiusthat is 15.6 inches long. Find the volume to the nearest tenth.A. 1019.4 in3 B. 7951.2 in3
C. 15,902.4 in3 D. 47,707.2 in3
8.1 mm2.3 mm
NAME DATE PERIOD
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© Glencoe/McGraw-Hill 768 Glencoe Geometry
Chapter 13 Quiz (Lesson 13–4)
1313
1.
2.
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4.
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1. Determine whether the cylinders are congruent, similar, or neither.
2. Determine whether solids having a scale factor of 1 arecongruent, similar, or neither.
3. The ratio of the heights of two similar cones is 2:3. Find theratio of their surface areas.
4. The scale factor of a model house is 1:100. The doors in thehouse are 84 inches high. How tall are the doors in the model?
5. Determine whether the statement A cone and a cylinder maybe similar is true or false.
10 m
12 m
3 m
4 m
NAME DATE PERIOD
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Chapter 13 Quiz (Lesson 13–5)
1313
1.
2.
3.
4.
5.
1. Find the coordinates of a pyramid with vertices A(2, 4, 0),B(3, 5, 0), C(�1, 6, 0), and D(2, 5, 3) under the translation (x, y, z) → (x � 3, y � 7, z � 5).
2. Graph the rectangular solid that contains the origin and B(5, 1, 3) as vertices.
For Questions 3–5, A(�2, 4, 9) and B(6, 1, 10).
3. Find the coordinates of the midpoint of A�B�.
4. Find the distance between A and B.
5. If B is the midpoint of A�C�, find the coordinates of C.
y
x
z
B
NAME DATE PERIOD
SCORE
Chapter 13 Mid-Chapter Test (Lessons 13–1 through 13–3)
1313
© Glencoe/McGraw-Hill 769 Glencoe Geometry
Ass
essm
ents
1. Choose the formula for the volume of a cylinder.
A. V � �r2h B. V � ��r
3
2h� C. V � 4�r2 D. V � �
4�3r3�
2. The volume of a cube is 216 cubic meters. Find the length of an edge.A. 72 m B. 36 m C. 12 m D. 6 m
3. A rectangular aquarium is 18 inches long and 12 inches wide and contains1620 cubic inches of water. Find the depth of the water.A. 15 in. B. 10 in.C. 7.5 in. D. 3.75 in.
4. How does the volume of a cone change when its radius is doubled?A. The volume is multiplied by 2. B. The volume is multiplied by 4.C. The volume is multiplied by 8. D. The volume is divided by 2.
5. The surface area of a sphere is equal to its volume. Find the radius.A. 1 unit B. 3 unitsC. 9 units D. cannot be determined
6.
7.
8.
9.
10.
NAME DATE PERIOD
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1.
2.
3.
4.
5.
Part II
6. Find the volume of this bead to the nearest centimeter.
7. Find the volume of a square pyramid whose slant height is 13 centimeters and whose base has sides that are each 24 centimeters long.
8. Find the volume to the nearest tenth.
9. A sphere has a surface area that is 169� square centimeters.Find the volume to the nearest tenth.
10. Find the volume.
4 in.
4 in.
4 in.
8 in.
42�
2 in.
2 cm2 cm
2 cm
1 cm
Part I Write the letter for the correct answer in the blank at the right of each question.
© Glencoe/McGraw-Hill 770 Glencoe Geometry
Chapter 13 Cumulative Review(Chapters 1–13)
1313
1.
2.
3.
4.
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6.
7.
8.
9.
10.
11.
12.
1. If �C and �D are congruent supplementary angles and m�C � 3x � 72, find x. (Lesson 2-8)
2. Determine the slope of the line that contains J(24, �5) andK(16, �18). (Lesson 3-3)
3. Classify �HJK by its sides if its vertices are H(6, �2),J(�9, �10), and K(�9, 6). (Lesson 4-1)
4. Find the measures of one exterior angle and one interior angleof a convex regular pentagon. (Lesson 8-1)
5. A 10-centimeter by 6-centimeter rectangle is enlarged by afactor of 3. What are the dimensions of the new rectangle?(Lesson 9-5)
6. In �A, mBC�� 2x � 16 and m�BAC � 5x � 98. Find x.
(Lesson 10-2)
7. Write an equation of a circle with center at (1, �2) and a diameter of 8 units. (Lesson 10-8)
8. Find the area of a rhombus with diagonals that are 24 centimeters and 78 centimeters long. (Lesson 11-2)
9. Write the number of faces and the shapes of the faces of a hexahedron. (Lesson 12-1)
10. Find the lateral area of a regular pentagonal prism if theheight of the prism is 9 centimeters and the perimeter of thepentagonal base is 35 centimeters. (Lesson 12-3)
11. Find the volume to the nearest tenth.(Lesson 13-1)
12. Find the volume to the nearest tenth.(Lesson 13-2)
12 in.7 in.
6 in.
3 m
12 m
NAME DATE PERIOD
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Standardized Test Practice (Chapters 1–13)
© Glencoe/McGraw-Hill 771 Glencoe Geometry
1. If D�G� bisects �EDF, which is a true statement? (Lesson 5-1)
A. B is the incenter of �DEF.B. DB � BGC. B�E� � B�F�D. B is equidistant from D�E� and D�F�.
2. If S�T� is a midsegment of �PQR,which is a true statement? (Lesson 6-4)
E. PQ � 2ST F. 2PQ � STG. 3PQ � 4ST H. 4PQ � 3ST
3. Which matrix can be used to find the coordinates of the image of a triangle reflected in the origin? (Lesson 9-7)
A. B. C. D.
4. Find the circumference of �G. (Lesson 10-1)
E. 9� in. F. 12� in.G. 15� in. H. 30� in.
5. If a line is tangent to a circle, then it is to the radiusdrawn to the point of tangency. (Lesson 10-5)
A. perpendicular B. parallelC. congruent D. not related
6. Find the area of a circle with a diameter of 28 meters. (Lesson 11-3)
E. 49� m2 F. 196� m2
G. 784� m2 H. 3136� m2
7. Which figures are needed to make a net for the solid? (Lesson 12-2)
A. 2 trapezoids and 4 rectanglesB. 6 rectanglesC. 4 trapezoids and 2 rectanglesD. 6 trapezoids
8. Find the volume of a right circular cone with a height of 14 inchesand a diameter of 10 inches to the nearest tenth. (Lesson 13-2)
E. 183.3 in3 F. 366.5 in3 G. 733.0 in3 H. 1466.1 in.
?
G9 in.
12 in.
1 00 1
�1 0 0 �1
�1 0 0 1
1 00 �1
Q
T
SP
R
E
GB
D
F
NAME DATE PERIOD
SCORE 1313
Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
1.
2.
3.
4.
5.
6.
7.
8. E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
Ass
essm
ents
© Glencoe/McGraw-Hill 772 Glencoe Geometry
Standardized Test Practice (continued)
9. Find m�HJK. (Lesson 10-6)
10. Find the y-coordinate of the image of A(3, �5)under a rotation of 180° clockwise about theorigin. (Lesson 9-3)
11. Find x so that the figures are similar. (Lesson 13-4)
8 cmx cm
9 cm
12 cm
JH
K276�
NAME DATE PERIOD
1313
Part 2: Grid In
Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
Part 3: Short Response
Instructions: Show your work or explain in words how you found your answer.
9. 10.
11.
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.
99 9 987654321
87654321
87654321
87654321
0 0 0
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.
99 9 987654321
87654321
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0 0 0
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.
99 9 987654321
87654321
87654321
87654321
12. Quadrilateral PQRS is inscribed in �O so that �S and �Qare opposite angles, m�Q � 10x � 11, and m�S � 6x � 27.Find x. (Lesson 10-4)
13. Find the area of quadrilateral CDEFif the distance from C to D�F� is 14meters. (Lesson 11-2)
14. A right cylinder has a height of 7 inches and a base with adiameter of 8 inches. What is the lateral area to the nearesttenth? (Lesson 12-4)
15. Find the volume of a hemisphere with a diameter of 18 feet tothe nearest tenth. (Lesson 13-3)
16. Determine the coordinates of the midpoint of the segmentjoining W(2, 4, �9) and X(�1, 7, �3). (Lesson 13-5)
7 m
12 m
D E
F
C
12.
13.
14.
15.
16.
4 2 5
3
Unit 4 Review (Chapters 11–13)
1313
© Glencoe/McGraw-Hill 773 Glencoe Geometry
Ass
essm
ents1. Determine whether BCDE with vertices B(3, 5), C(6, �2),
D(�4, �2), and E(�7, 5) is a square, rectangle, orparallelogram. Then find the area of BCDE.
2. If the trapezoid has an area of 152 square centimeters, find h.
3. A regular hexagon is inscribed in �P.Find the exact area of the shadedregion.
4. Find the area of the irregular figure.
5. Find the probability that a point selected at random lies in the shaded region.
For Questions 6 and 7, refer to the figure.
6. Identify the solid and name its bases.
7. Find the surface area of the solid to thenearest tenth if AB � 8, AC � 25,CF � 14, and EF � 25.
8. How many hexagons would be drawn in the net for ahexagonal prism?
9. Find the lateral area of a rectangular prism with base 4.8 inches by 6.2 inches and height 5.9 inches.
10. The surface area of a right cylinder is 324.7� square meters.Find the radius of the base of the cylinder if the height of thecylinder is 10.6 meters.
B
E F
C
A
D
x
y
O
(�1, 7) (2, 7)
(6, 2)(2, 1)(�2, 1)
P
18 in.
P
12 cm
20 cm
h
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 774 Glencoe Geometry
Unit 4 Review (continued)1313
11. Find the surface area of the regular pentagonal pyramid to the nearest tenth.
12. Mark is cutting colored paper to make conical party hats for his daughter’s birthday party. He wants to make them with a diameter of 9 inches and a height of 12 inches. What is the lateral area of one party hat?
13. To the nearest tenth, find the outer surface area of a bowl inthe shape of a perfect hemisphere with diameter 36 centimeters.
14. Sandra is packing a box with dimensions 54 inches by 78 inches by 42 inches. What is the maximum volume in cubicfeet that this box can hold? Round to the nearest tenth.
15. Find the volume of a cone with radius 11 inches and height 15 inches to the nearest tenth.
16. Which figure has the greater volume, the sphere or thecylinder?
17. Determine whether the pair of cones is similar, congruent,or neither.
18. Graph the rectangular solid that contains M(�1, �4, �3) andthe origin as vertices. Label the coordinates of each vertex.
24 cm7.5 cm
22.5 cm
36 cm
6 in.
2 in.
10 in.
9 in.
12 in.
4 ft
10 ft
11.
12.
13.
14.
15.
16.
17.
18.
y
x
z
(0, 0, 0)
(0, 0, �3)
(�1, �4, 0)(�1, 0, 0)
(�1, 0, �3)
M(�1, �4, �3)
(0, �4, 0)
(0, �4, �3)
NAME DATE PERIOD
Second Semester Test(Chapters 8–13)
1313
© Glencoe/McGraw-Hill 775 Glencoe Geometry
Ass
essm
entsFor Questions 1–17, write the letter for the correct answer in the blank
at the right of each question.
1. What are the coordinates of the intersection of the diagonals of parallelogramDEFG with vertices D(�1, �4), E(�2, 4), F(2, 6), and G(3, �2)?A. (0.5, 1) B. (0, 0)C. (0, 5) D. (2.5, 2)
2. If JKML is a rectangle, JN � 2a � 12, and LN � 5a � 48, find JM.A. 12 B. 24C. 52 D. 104
3. Which of the following statements is always true?A. A parallelogram is a rectangle. B. A square is a parallelogram.C. A rectangle is a square. D. A rhombus is a square.
4. If ABDC is a trapezoid, find AB so that E�F�is the median of ABDC.A. 13 B. 20C. 30.5 D. 61
5. Triangle LMN with vertices L(2, �5), M(�1, 0), N(0, 7) is reflected in the x-axis. Find the coordinates of the vertices of the reflected image.A. L�(2, �5), M�(�1, 0), N�(0, 7) B. L�(�2, �5), M�(1, 0), N�(0, 7)C. L�(2, 5), M�(�1, 0), N�(0, �7) D. L�(�5, 2), M�(0, �1), N�(7, 0)
6. Trapezoid WXYZ is rotated with respect to lines � and m . Determine the angle of rotation.A. 160° clockwiseB. 80° counterclockwiseC. 40° counterclockwiseD. 25° clockwise
7. Triangle HJK has vertices H(15, �9), J(�3, 0), and K(12, 6). Find thecoordinates of the vertices for a dilation centered at the origin with a scale
factor of ��13�.
A. H�(�45, 27), J�(9, 0), K�(�36, �18)B. H�(�5, 3), J�(1, 0), K�(�4, �2)C. H�(�9, 15), J�(0, �3), K�(6, 12)D. H�(15, 9), J�(�3, 0), K�(12, �6)
8. Find the exact circumference of �H.A. 42� B. 56�
C. 70� D. 84�H
42
56
W�
X�Y�
Z�
W
m �
XY
Z
A B
E F
C D34
27
J KN
L M
1.
2.
3.
4.
5.
6.
7.
8.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 776 Glencoe Geometry
Second Semester Test (continued)1313
9.
10.
11.
12.
13.
14.
15.
16.
17.
For Questions 9 and 10, refer to the figure.The diameter of �A is 40.
9. Find the exact value of BC if AC � 12.A. 16 B. 18C. 20 D. 24
10. If DF � 26�23�, find the exact value of EF so that D�F� is tangent to �A.
A. 8 B. 12 C. 13�13� D. 14�
23�
11. Which circle has equation (x � 5)2 � y2 � 81?A. �A with center at (5, 0), radius 5 B. �B with center at (0, 5), radius 9C. �C with center at (5, 0), radius 9 D. �D with center at (0, 5), radius 5
12. A parallelogram has a base of 21 inches, sides 14 inches, and height 9 inches.Find the area and perimeter of the parallelogram.A. area � 189 in2, perimeter � 70 in. B. area � 126 in2, perimeter � 70 in.C. area � 126 in2, perimeter � 49 in. D. area � 189 in2, perimeter � 79 in.
13. Find the area of a regular hexagon with a perimeter of 75 centimeters to thenearest tenth.A. 11.3 cm2 B. 12.5 cm2 C. 405.9 cm2 D. 450 cm2
14. Which of the following is a base of the figure?A. ONM B. ONJLC. OMKL D. KMNJ
15. Which of the following is the surface area to the nearest tenth of a rightcylinder with a height of 24 feet and a base diameter of 18 feet?A. 2714.3 ft2 B. 4750.1 ft2
C. 1357.2 ft2 D. 1866.1 ft2
16. Find the volume of the sphere to the nearest tenth.A. 289.5 m2 B. 463.2 m2
C. 1158.1 m2 D. 3705 m2
17. The solids are similar with a scale factor of 4:5.Find the ratio of the volumes of the twopyramids.A. 7:8 B. 12:15C. 16:25 D. 64:125
11.259
12 15
4.8 m
J
L
O
M
KN
A
B
CD
E F
NAME DATE PERIOD
Second Semester Test (continued)1313
© Glencoe/McGraw-Hill 777 Glencoe Geometry
Ass
essm
ents18. Find the sum of the measures of the interior angles and the
measure of one exterior angle of a convex regular 12-gon.
19. Find x and y so that ABCD is a parallelogram.
20. Determine whether JKLM with vertices J(0, �5), K(�4, �2),L(�1, 2), and M(3, �1) is a rhombus, a rectangle, or a square.List all that apply. Explain your reasoning.
21. Name the missing coordinates for the isosceles trapezoid.
22. Graph quadrilateral DEFG with vertices D(1, �4), E(3, �1),F(4, �2), and G(4, �4) and its image under the translation (x, y) → (x � 4, y � 3).
23. Find the measure of the preimage X�Y� if X�Y� � 204 in thedilated image and the scale factor is 8.
24. A charter boat travels a path due south at 20 miles per hour.The current is flowing from the east at 4 miles per hour. Whatis the resultant speed and direction of the boat? Round to thenearest tenth.
For Questions 25 and 26, refer to the figure. In �M, G�J� ⊥ M�L�.
25. Find the measure of each numbered angle in the circle.
26. Suppose a segment were drawn from K to G. What would the measure of �GKH be?
G
HJ
K
L
M22�1
2 3
4
x
y
(b, a)
(–c, 0)
(0, a)
(?, ?)
B C
A 4x � 30
2y � 1 3y � 5
x 6
D
18.
19.
20.
21.
22.
23.
24.
25.
26.
D�
E�F�
G�
D
EF
G
x
y
O
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 778 Glencoe Geometry
Second Semester Test (continued)1313
For Questions 27 and 28, refer to the figure.
27. If mVT�� 74 and mQU�
� 23, findm�P.
28. Solve for RS if VS � 32, ST � 25, and QS � 16.
29. Find the area of rhombus QRST with vertices Q(�2, 4),R(3, 1), S(�2, �2), and T(�7 , 1).
For Questions 30 and 31, refer to the figure.
30. Find the area of the figure to thenearest tenth.
31. What is the probability that a point selected at random lies on the shaded square?
32. Find the surface area of the prism.
33. A regular pyramid has a lateral area of 468 squarecentimeters and a slant height of 9 centimeters. Find theperimeter of the base of this pyramid.
34. Which has the greater surface area, a right cone with a baseradius of 6 meters and a height of 6 meters or a sphere with aradius of 6 meters?
35. A rectangular box has dimensions 45 inches by 74 inches by38 inches, and a cylindrical barrel has base diameter 50 inchesand height of 68 inches. Which container holds more volume?
36. Find the volume of the pyramid.
37. Determine the exact distance between A(�2, 5, �8) and Z(5, 7, 12).
5 cm
6 cm
12 cm
18
249
12 mm
4.5 mm
PU
Q
RT
V
S
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
NAME DATE PERIOD
Final Test1313
© Glencoe/McGraw-Hill 779 Glencoe Geometry
Ass
essm
entsFor Questions 1–26, write the letter for the correct answer in the blank
at the right of each question.
1. What are the coordinates of the midpoint of T�D� with T(�1, 5) and D(3, �9)?A. (2, 7) B. (2, �2) C. (1, 7) D. (1, �2)
2. Given A(2, 5), B(�7, 5), and C(102, 5), which statement has the same truthvalue as the statement A, B, and C are collinear?A. AC � 100 B. �ABC is an obtuse triangle.C. The perimeter of �ABC is 109 units. D. A�B� � B�C�
3. Gary knows that if two angles of a triangle are congruent, then the triangle isisosceles. He is given �FGH with �G � �H. With just this information, Garycan use the Law of Detachment to conclude which of the following?A. �F is the vertex angle of �FGH. B. �FGH is an isosceles triangle.C. m�G � m�H D. G�F� � H�F�
4. Which angles are consecutive interior angles?A. �1 and �4 B. �2 and �8C. �3 and �6 D. �3 and �5
5. Which equation represents a line that contains R(�5, 4) and S(7, 2)?A. 5y � 3x � 19 B. y � 6x � 40 C. 6y � �x � 19 D. 5y � �4x
6. Triangle RST is isosceles with vertex angle S. RS is six times a number, RT istwo times the number, and ST is twelve more than three times the number.Find the perimeter of �RST.A. 72 units B. 56 units C. 24 units D. 4 units
7. In the figure, W and V are the midpoints of X�Y�and Y�Z�, respectively, �YXV � �YZW, and XY � ZY. Which postulate or theorem can you use to prove �WXU � �VZU?A. AAS B. SSSC. SAS D. Congruence cannot be determined.
8. Given 3y � 8 � 14, which statement would you assume to write an indirectproof to show that y � 2?A. y � 2 B. 3y � 8 � 14 C. y � 2 D. 3y � 8 � 14
9. In �QRS, QR � 42 and RS � 50. Which of the following cannot be SQ?A. 9 B. 75 C. 84 D. 92
10. There are 135 girls in a club of 415 students. Find the ratio of girls to boys inthe club.A. 27:56 B. 13:41 C. 1:3 D. 3:17
Y
W X
ZVU
B1 2
3 45
68
7
m
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 780 Glencoe Geometry
Final Test (continued)1313
11.
12.
13.
14.
15.
16.
17.
18.
11. Mr. Trout’s class visited New York City with a 6-foot-tall scale model thatthey made of the Chrysler building. The class measured the model’s shadowat 1.44 inches and then measured the shadow of the Chrysler building at250.8 inches. What is the height of the actual building in feet?A. 125.4 ft B. 418 ft C. 836 ft D. 1045 ft
12. Slippery Ski Slope has an angle of depression of 9.5 degrees and is 412 meters long. Find thevertical drop of the slope to the nearest meter.A. 68 m B. 69 mC. 402 m D. 406 m
13. Find x to the nearest tenth.A. 49.2 B. 56.6C. 86.3 D. 98.4
14. If PQSR is a rhombus, and m�QRP � 73,find m�QSP.A. 73 B. 68C. 34 D. 17
15. What are the coordinates of B if BCDE is an isosceles trapezoid with verticesC(�3, 5), D(�1, 7), and E(1, 7)?A. B(1, 5) B. B(3, 5) C. B(3, �5) D. B(�1, 6)
16. Determine the direction of CD� to the nearest degree given C(�3, 10) and D(5, �12).A. 110° B. 290° C. 23 units D. 548 units
17. Triangle DEF has vertices D(4, 5), E(2, 7) and F(�3, 8). Which of the followingdemonstrates scalar multiplication to dilate �DEF so that its perimeter isdouble its original perimeter?
A. B. 2
C. 2 D.
18. A circle has a radius of 26 millimeters. What is the circumference of the circleto the nearest tenth?A. 81.7 mm B. 163.4 mm C. 530.9 mm D. 2123.7 mm
4 2 �35 7 8
1 00 1
4 2 �35 7 8
4 5 2 7�3 8
4 2 �35 7 8
0 22 0
P Q
SR
49�75
x
9.5�
? 412 m
NAME DATE PERIOD
Final Test (continued)1313
© Glencoe/McGraw-Hill 781 Glencoe Geometry
Ass
essm
ents19. Segments P�R� and Q�R� are tangent to �M.
Which of the following is true?A. �QPR � �PQR B. P�Q� � P�R�C. m�R � 75 D. PQ � QR
20. A group of 1800 single women in their twenties were asked to choose which type of date they would prefer from three choices. The results of the survey are recorded in the circle graph.What is the measure of the central anglerepresenting the “Rock Climbing” category?A. 28.8 B. 86.4C. 99.5 D. 111.6
21. Trapezoid JKLM has an area of 84 square centimeters. Find the height of JKLM.A. 2.2 cm B. 3.6 cmC. 7 cm D. 9 cm
22. Find the area of the parallelogram to the nearest tenth.A. 43.9 ft2 B. 56.2 ft2
C. 79.2 ft2 D. 112 ft2
23. What is the lateral area of the cylinder?A. 529� in2 B. 828� in2
C. 1886� in2 D. 9522� in2
24. Find the approximate amount of material needed to cover the entire solid.A. 371.6 m2 B. 678.6 m2
C. 923.6 m2 D. 1304.2 m2
25. A block of wood is cut with the dimensions shown. What is the volume of the wood?A. 2072 cm3 B. 2424 cm3
C. 3520 cm3 D. 7040 cm3
26. Two similar pyramids have slant heights of 15 and 24. What is the ratio ofthe surface areas of the two pyramids?A. 5:8 B. 25:64 C. 31:49 D. 125:512
20 cm
11 cm
32 cm
7 m
14 m
46 in.
18 in.
14 ft
8 ft45�
J K
LM
9 cm
15 cm
8%No response
ThemePark24%
RockClimbing
31%
DinnerCruise37%
Preferred Date
RM
Q
P 19.
20.
21.
22.
23.
24.
25.
26.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 782 Glencoe Geometry
Final Test (continued)1313
For Questions 27 and 28, refer to the figure.
27. Name a point in the interior of �KJG.
28. If m�GMK � 4x � 6 and m�KMJ � 3x � 32, find x and m�KMJ.
29. Identify the hypothesis and conclusion of the statement A circle with a radius of r has a circumference of 2�r.
30. Determine whether the following statement is always,sometimes, or never true.If two angles of a triangle measure 34 and 35, then the thirdangle must measure 111.
31. Graph the line that contains K(3, 4) and is perpendicular toGH��� containing G(�4, 3) and H(�1, 2).
32. Find x so that p || q.
33. If �RST � �BCD, find y and z.
For Questions 34–38, complete the proof.
Given: A�G� � E�H�C�A� � C�E��CGH � �CHG
Prove: �AGC � �EHCProof:Statements Reasons1. 1.2. G�C� � H�C� 2.3. 3.
39. When the medians of a triangle intersect, what is the point ofintersection called?
(Question 38)(Question 37)
(Question 36)
(Question 35)(Question 34)
A E
HG
C
y 9
z � 1
17
31
22
R T
S
DB
C
(x 8)� (2x � 8)�
p q
�
JM
G
HK
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
K(3, 4)
NAME DATE PERIOD
Final Test (continued)1313
© Glencoe/McGraw-Hill 783 Glencoe Geometry
Ass
essm
ents40. Write an inequality to describe the
possible values of y.
For Questions 41 and 42, refer to the figure. U�V� is a midsegment of�RST, and W�T� bisects �RTS.
41. If m�SRT � 7a and m�RUV � 29a,find a and m�VUT.
42. If RT � 8, UT � 4 and WT � 14,find XT.
43. Find a, b, and c.
44. In the figure, LK � 52. Find HKand LH.
45. Find the measure of each angle of the quadrilateral.
46. Find x and y so that quadrilateral LMNP is a parallelogram.
47. Determine how many lines of symmetry a regular pentagonhas. Then tell whether a regular pentagon has rotationalsymmetry.
48. Find the translation that moves triangle 1 to triangle 2 and then the translation that moves triangle 2 to triangle 3.
x
y
O
(�1, 4)
(2, �3)
(3, 0)
1
2
3
3x�
5y�39�
55�
P L
MN
(5x � 8)� (x 34)�
(3x 45)� (9x � 35)�G F
H E
135�KH
L
20
16 b
a
c
R TU
S
W V
X
98� 84�
10
88
y 740.
41.
42.
43.
44.
45.
46.
47.
48.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 784 Glencoe Geometry
Final Test (continued)1313
49. In �B, WV� � YT� and YZ � 28.What is the length of D�X�?
50. Find m�1 and m�2.
51. To the nearest tenth, find the area of a regular pentagon witha perimeter of 142 feet.
52. The diameter of the circle is 40 centimeters.Find the area of the circle. Then find theprobability that a point selected at randomlies within a shaded region of the circle.
53. Draw the corner view of the figure given the orthogonaldrawing.
54. Find the surface area of the regular pyramid to the nearest tenth.
55. Compare the volumes of the hemisphere and semicylinder. Which solid has the greater volume?
56. Determine the distance between H(�2, 4, �9) and J(3, �5, �12). Then state the coordinates of the midpoint of H�J�.
9 ft
9 ft 10 ft
12 cm
16 cm
top view left view front view right view
78�56�
43�
31�93�
59�
G46�
178�
1 2
B
V X
Z
Y
T
C
DW
49.
50.
51.
52.
53.
54.
55.
56.
NAME DATE PERIOD
Standardized Test PracticeStudent Record Sheet (Use with pages 724–725 of the Student Edition.)
1313
© Glencoe/McGraw-Hill A1 Glencoe Geometry
An
swer
s
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7
2 5 8
3 6 DCBADCBA
DCBADCBADCBA
DCBADCBADCBA
NAME DATE PERIOD
Part 1 Multiple ChoicePart 1 Multiple Choice
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 3 Open-EndedPart 3 Open-Ended
Solve the problem and write your answer in the blank.
For Questions 13 and 14, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.
9 13 14
10
11
12
13 (grid in)
14 (grid in)
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
Record your answers for Questions 15–16 on the back of this paper.
© Glencoe/McGraw-Hill A2 Glencoe Geometry
Stu
dy G
uid
e a
nd I
nte
rven
tion
Volu
mes
of
Pri
sms
and
Cyl
ind
ers
NA
ME
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AT
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__P
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IOD
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_
13-1
13-1
©G
lenc
oe/M
cGra
w-H
ill72
3G
lenc
oe G
eom
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Lesson 13-1
Vo
lum
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sT
he
mea
sure
of
the
amou
nt
of s
pace
th
at a
th
ree-
dim
ensi
onal
fig
ure
en
clos
es i
s th
e vo
lum
eof
th
e fi
gure
.Vol
um
e is
mea
sure
d in
un
its
such
as
cubi
c fe
et,c
ubi
c ya
rds,
or c
ubi
c m
eter
s.O
ne
cubi
c u
nit
is
the
volu
me
of a
cu
be
that
mea
sure
s on
e u
nit
on
eac
h e
dge.
27 c
ubic
fee
t �
1 cu
bic
yard
Volu
me
If a
pris
m h
as a
vol
ume
of V
cubi
c un
its,
a he
ight
of
hun
its,
of
a P
rism
and
each
bas
e ha
s an
are
a of
Bsq
uare
uni
ts,
then
V�
Bh.
cubi
c fo
otcu
bic
yard
Fin
d t
he
volu
me
of t
he
pri
sm.
V�
Bh
For
mul
a fo
r vo
lum
e
�(7
)(3)
(4)
B�
(7)(
3),
h�
4
�84
Mul
tiply.
Th
e vo
lum
e of
th
e pr
ism
is
84 c
ubi
cce
nti
met
ers.
7 cm
3 cm4
cm
Fin
d t
he
volu
me
of t
he
pri
sm i
f th
e ar
ea o
f ea
ch b
ase
is 6
.3sq
uar
e fe
et.
V�
Bh
For
mul
a fo
r vo
lum
e
�(6
.3)(
3.5)
B�
6.3,
h�
3.5
�22
.05
Mul
tiply.
Th
e vo
lum
e is
22.
05 c
ubi
c fe
et.
3.5
ft
base
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
volu
me
of e
ach
pri
sm.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
512
ft3
9 cm
3
3.4.
467.
7 ft
318
00 f
t3
5.6.
27 c
m3
84 y
d37 yd
4 yd
3 yd
4 cm
6 cm
2 cm
1.5
cm
10 ft
15 ft
12 ft
30�
15 ft12
ft
3 cm
4 cm
1.5
cm
8 ft
8 ft
8 ft
©G
lenc
oe/M
cGra
w-H
ill72
4G
lenc
oe G
eom
etry
Vo
lum
es o
f C
ylin
der
sT
he
volu
me
of a
cyl
inde
r is
th
e pr
odu
ct o
f th
e h
eigh
t an
d th
e ar
ea o
f th
e ba
se.T
he
base
of
a cy
lin
der
is a
cir
cle,
so t
he
area
of
th
e ba
se i
s �
r2.
Volu
me
of
If a
cylin
der
has
a vo
lum
e of
Vcu
bic
units
, a
heig
ht o
f h
units
, a
Cyl
ind
eran
d th
e ba
ses
have
rad
ii of
run
its,
then
V�
�r2
h.
r
h
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Volu
mes
of
Pri
sms
and
Cyl
ind
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-1
13-1
Fin
d t
he
volu
me
of t
he
cyli
nd
er.
V�
�r2
hV
olum
e of
a c
ylin
der
��
(3)2
(4)
r�
3, h
�4
�11
3.1
Sim
plify
.
Th
e vo
lum
e is
abo
ut
113.
1 cu
bic
cen
tim
eter
s.4 cm3 cm
Fin
d t
he
area
of
the
obli
qu
e cy
lin
der
.
Th
e ra
diu
s of
eac
h b
ase
is 4
in
ches
,so
the
area
of
the
base
is
16�
in2 .
Use
th
e P
yth
agor
ean
Th
eore
mto
fin
d th
e h
eigh
t of
th
e cy
lin
der.
h2
�52
�13
2P
ytha
gore
an T
heor
em
h2
�14
4S
impl
ify.
h�
12Ta
ke t
he s
quar
e ro
ot o
f ea
ch s
ide.
V�
�r2
hV
olum
e of
a c
ylin
der
��
(4)2
(12)
r�
4, h
�12
�60
3.2
in3
Sim
plify
.
8 in
.13 in
.
5 in
.
h
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
volu
me
of e
ach
cyl
ind
er.R
oun
d t
o th
e n
eare
st t
enth
.
1.2.
12.6
ft3
226.
2 cm
3
3.4.
84.8
ft3
6283
.2 f
t3
5.6.
652.
4 cm
312
.6 y
d3
1 yd
4 yd
10 c
m
13 c
m
20 ft
20 ft
12 ft
1.5
ft
18 c
m2
cm2
ft
1 ft
Answers (Lesson 13-1)
© Glencoe/McGraw-Hill A3 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Volu
mes
of
Pri
sms
and
Cyl
ind
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-1
13-1
©G
lenc
oe/M
cGra
w-H
ill72
5G
lenc
oe G
eom
etry
Lesson 13-1
Fin
d t
he
volu
me
of e
ach
pri
sm o
r cy
lin
der
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
2304
cm
396
ft3
3.4.
90 m
352
80 in
3
5.6.
16,2
57.7
mm
322
6.2
yd3
Fin
d t
he
volu
me
of e
ach
ob
liq
ue
pri
sm o
r cy
lin
der
.Rou
nd
to
the
nea
rest
ten
th i
fn
eces
sary
.
7.8.
1224
cm
3
141.
4 in
3
5 in
.
3 in
.17
cm
18 c
m
4 cm
6 yd 10
yd
15 m
m23
mm
16 in
.22
in.
34 in
.
3 m
5 m
13 m
6 ft
8 ft
2 ft
18 c
m
16 c
m8 cm
©G
lenc
oe/M
cGra
w-H
ill72
6G
lenc
oe G
eom
etry
Fin
d t
he
volu
me
of e
ach
pri
sm o
r cy
lin
der
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
2040
m3
97.4
in3
3.4.
3518
.6 m
m3
923.
6 ft
3
5.6.
2600
yd
360
31.9
cm
3
AQ
UA
RIU
MF
or E
xerc
ises
7–9
,use
th
e fo
llow
ing
info
rmat
ion
.Rou
nd
an
swer
s to
the
nea
rest
ten
th.
Mr.
Gu
tier
rez
purc
has
ed a
cyl
indr
ical
aqu
ariu
m f
or h
is o
ffic
e.T
he
aqu
ariu
m h
as a
hei
ght
of
25�1 2�
inch
es a
nd
a ra
diu
s of
21
inch
es.
7.W
hat
is
the
volu
me
of t
he
aqu
ariu
m i
n c
ubi
c fe
et?
5.1
ft3
8.If
th
ere
are
7.48
gal
lon
s in
a c
ubi
c fo
ot,h
ow m
any
gall
ons
of w
ater
doe
s th
e aq
uar
ium
hol
d?
38.2
gal
9.If
a c
ubi
c fo
ot o
f w
ater
wei
ghs
abou
t 62
.4 p
oun
ds,w
hat
is
the
wei
ght
of t
he
wat
er i
n t
he
aqu
ariu
m t
o th
e n
eare
st f
ive
pou
nds
?
2385
lb
30 c
m
8 cm
13 y
d
20 y
d
10 y
d
7 ft
25 ft
16 m
m17
.5 m
m
5 in
.
5 in
.
5 in
.
9 in
.17
m10
m
26 mP
ract
ice (
Ave
rag
e)
Volu
mes
of
Pri
sms
and
Cyl
ind
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-1
13-1
Answers (Lesson 13-1)
© Glencoe/McGraw-Hill A4 Glencoe Geometry
Readin
g t
o L
earn
Math
em
ati
csVo
lum
es o
f P
rism
s an
d C
ylin
der
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-1
13-1
©G
lenc
oe/M
cGra
w-H
ill72
7G
lenc
oe G
eom
etry
Lesson 13-1
Pre-
Act
ivit
yH
ow i
s m
ath
emat
ics
use
d i
n c
omic
s?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 13
-1 a
t th
e to
p of
pag
e 68
8 in
you
r te
xtbo
ok.
In t
he
cart
oon
,wh
y w
as S
hoe
con
fuse
d w
hen
th
e te
ach
er s
aid
the
clas
s w
asgo
ing
to d
iscu
ss v
olu
mes
?S
amp
le a
nsw
er:T
he
teac
her
was
refe
rrin
g t
o t
he
mat
hem
atic
al m
ean
ing
of
volu
me,
wh
ich
is t
he
amo
un
t o
f sp
ace
encl
ose
d b
y a
thre
e-d
imen
sio
nal
fig
ure
.Sh
oe
was
th
inki
ng
ab
ou
t vo
lum
es a
s b
oo
ks,w
hic
h is
a c
om
ple
tely
dif
fere
nt
mea
nin
g o
f th
e w
ord
.
Rea
din
g t
he
Less
on
1.In
eac
h ca
se,w
rite
a f
orm
ula
for
the
volu
me
Vof
the
sol
id i
n te
rms
of t
he g
iven
var
iabl
es.
a.a
rect
angu
lar
box
wit
h l
engt
h a
,wid
th b
,an
d h
eigh
t c
V�
abc
b.
a re
ctan
gula
r bo
x w
ith
squ
are
base
s w
ith
sid
e le
ngt
h x
,an
d w
ith
hei
ght
yV
�x2
yc.
a cu
be w
ith
edg
es o
f le
ngt
h e
V�
e3
d.
a tr
ian
gula
r pr
ism
wh
ose
base
s ar
e is
osce
les
righ
t tr
ian
gles
wit
h l
egs
of l
engt
h x
,an
dw
hos
e h
eigh
t is
yV
��1 2� x
2 yo
r V
��x 22 y �
e.a
pris
m w
hos
e ba
ses
are
regu
lar
poly
gon
s w
ith
per
imet
er P
and
apot
hem
a,a
nd
wh
ose
hei
ght
is h
V�
�1 2� aP
ho
r V
��aP
2h �
f.a
cyli
nde
r w
hos
e ba
ses
each
hav
e ra
diu
s r,
and
wh
ose
hei
ght
is t
hre
e ti
mes
th
e ra
diu
sof
th
e ba
ses
V�
3�r3
g.a
regu
lar
octa
gon
al p
rism
in
wh
ich
eac
h b
ase
has
sid
es o
f le
ngt
h s
and
apot
hem
a,
and
wh
ose
hei
ght
is t
V�
4ast
h.
a cy
lin
der
wit
h h
eigh
t h
wh
ose
base
s ea
ch h
ave
diam
eter
d
V�
���d 2� �2 h
or
V�
��d 42 h �
or
V�
�1 4� �d
2 h
i.an
obl
iqu
e cy
lin
der
wh
ose
base
s h
ave
radi
us
aan
d w
hos
e h
eigh
t is
bV
��
a2b
j.a
regu
lar
hex
agon
al p
rism
wh
ose
base
s h
ave
side
len
gth
s,a
nd
wh
ose
hei
ght
is h
V�
�3 2� s2 h
�3�
Hel
pin
g Y
ou
Rem
emb
er2.
A g
ood
way
to
rem
embe
r a
mat
hem
atic
al c
once
pt i
s to
exp
lain
it
to s
omeo
ne e
lse.
Sup
pose
that
you
r yo
un
ger
sist
er,w
ho
is i
n e
igh
th g
rade
,is
hav
ing
trou
ble
un
ders
tan
din
g w
hy
squ
are
un
its
are
use
d to
mea
sure
are
a,bu
t cu
bic
un
its
are
nee
ded
to m
easu
re v
olu
me.
How
can
you
exp
lain
th
is t
o h
er i
n a
way
th
at w
ill
mak
e it
eas
y fo
r h
er t
o u
nde
rsta
nd
and
rem
embe
r th
e co
rrec
t u
nit
s to
use
?S
amp
le a
nsw
er:
Are
a m
easu
res
the
amo
un
t o
f sp
ace
insi
de
a tw
o-d
imen
sio
nal
fig
ure
,wh
ile v
olu
me
mea
sure
sth
e am
ou
nt
of
spac
e in
sid
e a
thre
e-d
imen
sio
nal
fig
ure
.A t
wo
-dim
ensi
on
alfi
gu
re c
an b
e co
vere
d w
ith
sm
all s
qu
ares
,wh
ich
rep
rese
nt
squ
are
un
its,
wh
ile a
th
ree-
dim
ensi
on
al f
igu
re c
an b
e fi
lled
wit
h s
mal
l cu
bes
,wh
ich
rep
rese
nt
cub
ic u
nit
s.
©G
lenc
oe/M
cGra
w-H
ill72
8G
lenc
oe G
eom
etry
Vis
ible
Su
rfac
e A
rea
Use
pap
er,s
ciss
ors,
and
tap
e to
mak
e fi
ve c
ub
es t
hat
hav
e on
e-in
ch e
dge
s.A
rran
ge t
he
cub
es t
o fo
rm e
ach
sh
ape
show
n.T
hen
fin
d t
he
volu
me
and
th
e vi
sib
le s
urf
ace
area
.In
oth
er w
ord
s,d
o n
ot i
ncl
ud
e th
e ar
ea o
f su
rfac
eco
vere
d b
y ot
her
cu
bes
or
by
the
tab
le o
r d
esk
.
1.2.
volu
me
�4
in3
volu
me
�4
in3
surf
ace
area
�14
in2
surf
ace
area
�15
in2
3.4.
5.
volu
me
�5
in3
volu
me
�5
in3
volu
me
�5
in3
surf
ace
area
�17
in2
surf
ace
area
�19
in2
surf
ace
area
�19
in2
6.F
ind
the
volu
me
and
the
visi
ble
surf
ace
area
of
the
figu
re a
t th
e ri
ght.
volu
me
�12
4 in
3
surf
ace
area
�15
8 in
2
4 in
.
4 in
.
3 in
.
3 in
.
3 in
.
8 in
.
3 in
. 5 in
.
5 in
.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-1
13-1
Answers (Lesson 13-1)
© Glencoe/McGraw-Hill A5 Glencoe Geometry
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Volu
mes
of
Pyr
amid
s an
d C
on
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-2
13-2
©G
lenc
oe/M
cGra
w-H
ill72
9G
lenc
oe G
eom
etry
Lesson 13-2
Vo
lum
es o
f Py
ram
ids
Th
is f
igu
re s
how
s a
pris
m a
nd
a py
ram
id
that
hav
e th
e sa
me
base
an
d th
e sa
me
hei
ght.
It i
s cl
ear
that
th
e vo
lum
e of
th
e py
ram
id i
s le
ss t
han
th
e vo
lum
e of
th
e pr
ism
.Mor
e sp
ecif
ical
ly,
the
volu
me
of t
he
pyra
mid
is
one-
thir
d of
th
e vo
lum
e of
th
e pr
ism
.
Volu
me
of
If a
pyra
mid
has
a v
olum
e of
Vcu
bic
units
, a
heig
ht o
f h
units
, a
Pyr
amid
and
a ba
se w
ith a
n ar
ea o
f B
squa
re u
nits
, th
en V
��1 3� B
h.
Fin
d t
he
volu
me
of t
he
squ
are
pyr
amid
.
V�
�1 3� Bh
Vol
ume
of a
pyr
amid
� �1 3� (
8)(8
)10
B�
(8)(
8),
h�
10
�21
3.3
Mul
tiply
.
Th
e vo
lum
e is
abo
ut
213.
3 cu
bic
feet
.
Fin
d t
he
volu
me
of e
ach
pyr
amid
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
320
ft3
120
ft3
3.4.
110.
9 cm
356
1.2
ft3
5.6.
1200
in3
64 y
d3
6 yd
8 yd
5 yd
15 in
.
15 in
.
16 in
.
18 ft
regu
lar
hexa
gon
6 ft
4 cm
8 cm
12 c
m
10 ft
6 ft
15 ft
12 ft
8 ft
10 ft
8 ft
8 ft
10 ft
Exer
cises
Exer
cises
Exam
ple
Exam
ple
©G
lenc
oe/M
cGra
w-H
ill73
0G
lenc
oe G
eom
etry
Vo
lum
es o
f C
on
esF
or a
con
e,th
e vo
lum
e is
on
e-th
ird
the
prod
uct
of
the
hei
ght
and
the
base
.Th
e ba
se o
f a
con
e is
a c
ircl
e,so
th
e ar
ea o
f th
e ba
se i
s �
r2.
Volu
me
of
a R
igh
t If
a co
ne h
as a
vol
ume
of V
cubi
c un
its,
a he
ight
of
hun
its,
Cir
cula
r C
on
ean
d th
e ar
ea o
f th
e ba
se is
Bsq
uare
uni
ts,
then
V�
�1 3� Bh.
Th
e sa
me
form
ula
can
be
use
d to
fin
d th
e vo
lum
e of
obl
iqu
e co
nes
.
Fin
d t
he
volu
me
of t
he
con
e.
V�
�1 3� �r2
hV
olum
e of
a c
one
� �1 3� �
(5)2
12r
�5,
h�
12
�31
4.2
Sim
plify
.
Th
e vo
lum
e of
th
e co
ne
is a
bou
t 31
4.2
cubi
c ce
nti
met
ers.
Fin
d t
he
volu
me
of e
ach
con
e.R
oun
d t
o th
e n
eare
st t
enth
.
1.2.
301.
6 cm
367
0.2
ft3
3.4.
1131
.0 in
313
32.9
yd
3
5.6.
2513
.3 f
t337
9.1
cm3
16 c
m
45�
26 ft
20 ft
45�
18 y
d 20 y
d30
in.
12 in
.
8 ft
10 ft
6 cm
10 c
m
12 c
m
5 cm
r
h
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Volu
mes
of
Pyr
amid
s an
d C
on
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-2
13-2
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 13-2)
© Glencoe/McGraw-Hill A6 Glencoe Geometry
Skil
ls P
ract
ice
Volu
mes
of
Pyr
amid
s an
d C
on
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-2
13-2
©G
lenc
oe/M
cGra
w-H
ill73
1G
lenc
oe G
eom
etry
Lesson 13-2
Fin
d t
he
volu
me
of e
ach
pyr
amid
or
con
e.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
66.7
ft3
74.7
cm
3
3.4.
357.
8 in
337
69.9
m3
5.6.
1231
.5 y
d3
1210
.6 m
m3
Fin
d t
he
volu
me
of e
ach
ob
liq
ue
pyr
amid
or
con
e.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
7.8.
32 f
t345
2.4
cm3
12 c
m6 cm
4 ft
4 ft
6 ft
66�
18 m
m
25 y
d
14 y
d
25 m12
m
8 in
.10
in.
14 in
.
4 cm
7 cm
8 cm
5 ft
5 ft
8 ft
©G
lenc
oe/M
cGra
w-H
ill73
2G
lenc
oe G
eom
etry
Fin
d t
he
volu
me
of e
ach
pyr
amid
or
con
e.R
oun
d t
o th
e n
eare
st t
enth
if
nec
essa
ry.
1.2.
343.
1 yd
323
95.8
cm
3
3.4.
1419
.4 f
t311
04.6
mm
3
5.6.
132
in3
4688
.3 f
t3
7.C
ON
STR
UC
TIO
NM
r.G
anty
bui
lt a
con
ical
sto
rage
she
d.T
he b
ase
of t
he s
hed
is 4
met
ers
in d
iam
eter
,an
d th
e h
eigh
t of
th
e sh
ed i
s 3.
8 m
eter
s.W
hat
is
the
volu
me
of t
he
shed
?
abo
ut
15.9
m3
8.H
ISTO
RYT
he
star
t of
th
e py
ram
id a
ge b
egan
wit
h K
ing
Zos
er’s
pyr
amid
,ere
cted
in
th
e27
th c
entu
ry B
.C.I
n i
ts o
rigi
nal
sta
te,i
t st
ood
62 m
eter
s h
igh
wit
h a
rec
tan
gula
r ba
seth
at m
easu
red
140
met
ers
by 1
18 m
eter
s.F
ind
the
volu
me
of t
he
orig
inal
pyr
amid
.
abo
ut
341,
413.
3 m
3
37 ft
11 ft
6 in
.6
in.
11 in
.
52�
12 m
m19
ft
9 ft
12.5
cm
25 c
m
23 c
m
9.2
yd9.
2 yd
13 y
d
Pra
ctic
e (
Ave
rag
e)
Volu
mes
of
Pyr
amid
s an
d C
on
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-2
13-2
Answers (Lesson 13-2)
© Glencoe/McGraw-Hill A7 Glencoe Geometry
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csVo
lum
es o
f P
yram
ids
and
Co
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-2
13-2
©G
lenc
oe/M
cGra
w-H
ill73
3G
lenc
oe G
eom
etry
Lesson 13-2
Pre-
Act
ivit
yH
ow d
o ar
chit
ects
use
geo
met
ry?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 13
-2 a
t th
e to
p of
pag
e 69
6 in
you
r te
xtbo
ok.
In a
ddit
ion
to
refl
ecti
ng
mor
e li
ght,
wh
y do
you
th
ink
the
arch
itec
t of
th
eT
rans
amer
ica
Pyr
amid
may
hav
e de
sign
ed t
he b
uild
ing
as a
squ
are
pyra
mid
rath
er t
han
a r
ecta
ngu
lar
pris
m?
Sam
ple
an
swer
:Th
e p
yram
id is
mo
re u
nu
sual
an
d h
as a
mo
re d
ram
atic
ap
pea
ran
ce,s
o it
attr
acts
mo
re a
tten
tio
n.W
ith
th
e sh
arp
po
int
at t
he
top
,it
seem
s to
so
ar u
p in
to t
he
sky.
Rea
din
g t
he
Less
on
1.In
eac
h c
ase,
two
soli
ds a
re d
escr
ibed
.Det
erm
ine
wh
eth
er t
he
firs
t so
lid
or t
he
seco
nd
soli
d h
as t
he
grea
ter
volu
me,
or i
f th
e tw
o so
lids
hav
e th
e sa
me
volu
me.
(An
swer
by
wri
tin
g fi
rst,
seco
nd
,or
sam
e.)
a.F
irst
sol
id:A
rec
tan
gula
r pr
ism
wit
h l
engt
h x
,wid
th y
,an
d h
eigh
t z
Sec
ond
soli
d:A
rec
tan
gula
r pr
ism
wit
h l
engt
h 2
x,w
idth
y,h
eigh
t z
seco
nd
b.
Fir
st s
olid
:a r
ecta
ngu
lar
pris
m t
hat
has
a s
quar
e ba
se w
ith
sid
e le
ngt
h x
and
that
has
hei
ght
yS
econ
d so
lid:a
squ
are
pyra
mid
who
se b
ase
has
side
leng
th x
and
that
has
hei
ght
yfir
stc.
Fir
st s
olid
:a r
igh
t co
ne
wh
ose
base
has
rad
ius
xan
d th
at h
as h
eigh
t y
Sec
ond
soli
d:an
obl
iqu
e co
ne
wh
ose
base
has
rad
ius
xan
d th
at h
as h
eigh
t y
sam
ed
.F
irst
sol
id:a
con
e w
hos
e ba
se h
as r
adiu
s x,
and
wh
ose
hei
ght
is y
Sec
ond
soli
d:a
cyli
nde
r w
hos
e ba
ses
hav
e ra
diu
s x,
and
wh
ose
hei
ght
is y
seco
nd
e.F
irst
sol
id:a
con
e w
hos
e ba
se h
as r
adiu
s x
and
wh
ose
hei
ght
is y
Sec
ond
solid
:a s
quar
e py
ram
id w
hose
bas
e ha
s si
de le
ngth
xan
d w
hose
hei
ght
is y
first
2.S
upp
ly t
he
mis
sin
g n
um
bers
to
form
tru
e st
atem
ents
.
a.If
th
e le
ngt
h,w
idth
,an
d h
eigh
t of
a r
ecta
ngu
lar
box
are
all
dou
bled
,its
vol
um
e w
ill
be m
ult
ipli
ed b
y .
b.
If t
he
radi
us
of a
cyl
inde
r is
tri
pled
an
d th
e h
eigh
t is
un
chan
ged,
the
volu
me
wil
l be
mu
ltip
lied
by
.
c.In
a s
quar
e py
ram
id,i
f th
e si
de l
engt
h o
f th
e ba
se i
s m
ult
ipli
ed b
y 1.
5 an
d th
e h
eigh
t
is d
oubl
ed,t
he
volu
me
wil
l be
mu
ltip
lied
by
.
d.
In a
con
e,if
th
e ra
diu
s of
th
e ba
se i
s tr
iple
d an
d th
e h
eigh
t is
dou
bled
,th
e vo
lum
e
wil
l be
mu
ltip
lied
by
.
e.In
a c
ube
,if
the
edge
len
gth
is
mu
ltip
lied
by
5,th
e vo
lum
e w
ill
be m
ult
ipli
ed b
y .
Hel
pin
g Y
ou
Rem
emb
er
3.M
any
stu
den
ts f
ind
it e
asie
r to
rem
embe
r m
ath
emat
ical
for
mu
las
if t
hey
can
pu
t th
emin
wor
ds.U
se w
ords
to
desc
ribe
in
on
e se
nte
nce
how
to
fin
d th
e vo
lum
e of
an
y py
ram
idor
cyl
inde
r.S
amp
le a
nsw
er:
Mu
ltip
ly t
he
area
of
the
bas
e by
th
e h
eig
ht
and
div
ide
by 3
.
125
18
4.5
9
8
©G
lenc
oe/M
cGra
w-H
ill73
4G
lenc
oe G
eom
etry
Fru
stu
ms
A f
rust
um
is a
fig
ure
for
med
wh
en a
pla
ne
inte
rsec
ts a
pyr
amid
or
con
e so
th
at t
he
plan
e is
par
alle
l to
th
e so
lid’
s ba
se.T
he
fru
stu
m i
s th
e pa
rt o
f th
e so
lid
betw
een
th
e pl
ane
and
the
base
.To
fin
d th
evo
lum
e of
a f
rust
um
,th
e ar
eas
of b
oth
bas
es m
ust
be
calc
ula
ted
and
use
d in
th
e fo
rmu
la
V�
�1 3� h(B
1�
B2
��
B1B
2�
),w
her
e h
�h
eigh
t (p
erpe
ndi
cula
r di
stan
ce b
etw
een
th
e ba
ses)
,B
1�
area
of
top
base
,an
d B
2�
area
of
bott
om b
ase.
Des
crib
e th
e sh
ape
of t
he
bas
es o
f ea
ch f
rust
um
.Th
en f
ind
th
e vo
lum
e.R
oun
d t
o th
e n
eare
st t
enth
.
1.2.
rect
ang
les;
617.
5 cm
3
circ
les;
335.
8 in
3
3.4.
trap
ezo
ids;
151.
6 m
3
circ
les;
3480
.9 f
t3
12 ft
13 ft
7 ft
8 m
6 m
12 m
4.5
m2.
25 m3
m
5 m
3 in
.
7.5
in.
4.5
in.
13 c
m 6 cm
9 cm
5 cm
19.5
cm
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-2
13-2
Answers (Lesson 13-2)
© Glencoe/McGraw-Hill A8 Glencoe Geometry
Stu
dy G
uid
e a
nd I
nte
rven
tion
Volu
mes
of
Sp
her
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-3
13-3
©G
lenc
oe/M
cGra
w-H
ill73
5G
lenc
oe G
eom
etry
Lesson 13-3
Vo
lum
es o
f Sp
her
esA
sph
ere
has
on
e ba
sic
mea
sure
men
t,th
e le
ngt
h o
f it
s ra
diu
s.If
you
kn
ow t
he
radi
us
of a
sph
ere,
you
can
cal
cula
te
its
volu
me.
Volu
me
of
a S
ph
ere
If a
sphe
re h
as a
vol
ume
of V
cubi
c un
its a
nd a
rad
ius
of r
units
, th
en V
��4 3� �
r3.
Fin
d t
he
volu
me
of a
sp
her
e w
ith
rad
ius
8 ce
nti
met
ers.
V�
�4 3� �r3
Vol
ume
of a
sph
ere
��4 3� �
(8)3
r�
8
�21
44.7
Sim
plify
.
Th
e vo
lum
e is
abo
ut
2144
.7 c
ubi
c ce
nti
met
ers.
A s
ph
ere
wit
h r
adiu
s 5
inch
es j
ust
fit
s in
sid
e a
cyli
nd
er.W
hat
is
the
dif
fere
nce
bet
wee
n t
he
volu
me
of t
he
cyli
nd
er a
nd
th
e vo
lum
e of
th
e sp
her
e? R
oun
d t
o th
e n
eare
st
cub
ic i
nch
.T
he
base
of
the
cyli
nde
r is
25�
in2
and
the
hei
ght
is 1
0 in
.,so
th
e vo
lum
e of
th
e cy
lin
der
is 2
50�
in3 .
Th
e vo
lum
e of
th
e sp
her
e is
�4 3� �(5
)3
or �50
30� �in
3 .T
he
diff
eren
ce i
n t
he
volu
mes
is
250�
��50
30� �or
abo
ut
262
in3 .
Fin
d t
he
volu
me
of e
ach
sol
id.R
oun
d t
o th
e n
eare
st t
enth
.
1.2.
3.
523.
6 ft
345
2.4
in3
8578
.6 in
3
4.5.
6.
268.
1 cm
357
6.0
in3
243.
9 in
3
7.A
hem
isph
ere
wit
h r
adiu
s 16
cen
tim
eter
s ju
st f
its
insi
de a
rec
tan
gula
r pr
ism
.Wh
at i
sth
e di
ffer
ence
bet
wee
n t
he
volu
me
of t
he
pris
m a
nd
the
volu
me
of t
he
hem
isph
ere?
Rou
nd
to t
he
nea
rest
cu
bic
cen
tim
eter
.78
05 c
m3
8 in
.di
ffere
nce
betw
een
volu
me
of c
ube
and
volu
me
of s
pher
e
13 in
.5
in.
8 cm
16 in
.
6 in
.
5 ft
5 in
.
5 in
.
5 in
.5
in.
8 cmr
Exer
cises
Exer
cises
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
©G
lenc
oe/M
cGra
w-H
ill73
6G
lenc
oe G
eom
etry
Solv
e Pr
ob
lem
s In
volv
ing
Vo
lum
es o
f Sp
her
esIf
you
wan
t to
kn
ow i
f a
sph
ere
can
be
pack
ed i
nsi
de a
not
her
con
tain
er,o
r if
you
wan
t to
com
pare
th
e ca
paci
ty o
f a
sph
ere
and
anot
her
sh
ape,
you
can
com
pare
vol
um
es.
Com
par
e th
e vo
lum
es o
f th
e sp
her
e an
d
the
cyli
nd
er.D
eter
min
e w
hic
h q
uan
tity
is
grea
ter.
V�
�4 3� �r3
Vol
ume
of s
pher
eV
��
r2h
Vol
ume
of c
ylin
der
��
r2(1
.5r)
h�
1.5r
�1.
5�r3
Sim
plify
.
Com
pare
�4 3� �r3
wit
h 1
.5�
r3.S
ince
�4 3�is
les
s th
an 1
.5,i
t fo
llow
s th
at
the
volu
me
of t
he
sph
ere
is l
ess
than
th
e vo
lum
e of
th
e cy
lin
der.
Com
par
e th
e vo
lum
e of
a s
ph
ere
wit
h r
adiu
s r
to t
he
volu
me
of e
ach
fig
ure
bel
ow.
Wh
ich
fig
ure
has
a g
reat
er v
olu
me?
1.2.
Th
e vo
lum
e o
f th
e h
emis
ph
ere
Th
e vo
lum
e o
f th
e sp
her
e is
gre
ater
.is
gre
ater
.
3.4.
Th
e vo
lum
e o
f th
e sp
her
eT
he
volu
me
of
the
sph
ere
is
gre
ater
.is
gre
ater
.
5.6.
Th
e vo
lum
e o
f th
e cy
lind
erca
nn
ot
be
det
erm
ined
(If
a�
0.63
,is
gre
ater
.th
e vo
lum
e o
f th
e h
emis
ph
ere
isg
reat
er.I
f a
�0.
63,t
he
volu
me
of
the
sph
ere
is g
reat
er.)
2ar
3r
r
r3r
r
rr
rr 2
2r
r1.
5r
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Volu
mes
of
Sp
her
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-3
13-3
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 13-3)
© Glencoe/McGraw-Hill A9 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Volu
mes
of
Sp
her
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-3
13-3
©G
lenc
oe/M
cGra
w-H
ill73
7G
lenc
oe G
eom
etry
Lesson 13-3
Fin
d t
he
volu
me
of e
ach
sp
her
e or
hem
isp
her
e.R
oun
d t
o th
e n
eare
st t
enth
.
1.T
he
radi
us
of t
he
sph
ere
is 9
cen
tim
eter
s.
3053
.6 c
m3
2.T
he
diam
eter
of
the
sph
ere
is 1
0 in
ches
.
523.
6 in
3
3.T
he
circ
um
fere
nce
of
the
sph
ere
is 2
6 m
eter
s.
296.
8 m
3
4.T
he
radi
us
of t
he
hem
isph
ere
is 7
fee
t.
718.
4 ft
3
5.T
he
diam
eter
of
the
hem
isph
ere
is 1
2 ki
lom
eter
s.
452.
4 km
3
6.T
he
circ
um
fere
nce
of
the
hem
isph
ere
is 4
8 ya
rds.
933.
8 yd
3
7.8.
2226
.1 c
m3
446,
091.
2 ft
3
9.10
.
190.
9 in
378
1.7
m3
14.4
m
4.5
in.
94.8
ft16
.2 c
m
©G
lenc
oe/M
cGra
w-H
ill73
8G
lenc
oe G
eom
etry
Fin
d t
he
volu
me
of e
ach
sp
her
e or
hem
isp
her
e.R
oun
d t
o th
e n
eare
st t
enth
.
1.T
he
radi
us
of t
he
sph
ere
is 1
2.4
cen
tim
eter
s.
7986
.4 c
m3
2.T
he
diam
eter
of
the
sph
ere
is 1
7 fe
et.
2572
.4 f
t3
3.T
he
circ
um
fere
nce
of
the
sph
ere
is 3
8 m
eter
s.
926.
6 m
3
4.T
he
diam
eter
of
the
hem
isph
ere
is 2
1 in
ches
.
2424
.5 in
3
5.T
he
circ
um
fere
nce
of
the
hem
isph
ere
is 1
8 m
illi
met
ers.
49.2
mm
3
6.7.
7832
.9 f
t332
94.8
cm
3
8.9.
8578
.6 m
367
1.3
mm
3
10.P
AC
KA
GIN
GA
mbe
r pl
ans
to s
hip
a m
ini-
bask
etba
ll s
he
bou
ght
for
her
nep
hew
.Th
eci
rcu
mfe
ren
ce o
f th
e ba
ll i
s 24
in
ches
an
d th
e pa
ckag
e sh
e w
ants
to
ship
it
in i
s a
rect
angu
lar
box
that
mea
sure
s 8
inch
es �
8 in
ches
�9
inch
es.W
ill
the
bask
etba
ll f
it i
nth
e bo
x? E
xpla
in.
Yes;
the
dia
met
er o
f th
e b
all i
s ab
ou
t 7.
64 in
.,so
th
e b
all w
ill f
it in
th
e b
ox.
C �
43
mm
32 m
C �
58
cm12
.32
ft
Pra
ctic
e (
Ave
rag
e)
Volu
mes
of
Sp
her
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-3
13-3
Answers (Lesson 13-3)
© Glencoe/McGraw-Hill A10 Glencoe Geometry
Readin
g t
o L
earn
Math
em
ati
csVo
lum
es o
f S
ph
eres
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-3
13-3
©G
lenc
oe/M
cGra
w-H
ill73
9G
lenc
oe G
eom
etry
Lesson 13-3
Pre-
Act
ivit
yH
ow c
an y
ou f
ind
th
e vo
lum
e of
Ear
th?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 13
-3 a
t th
e to
p of
pag
e 70
2 in
you
r te
xtbo
ok.
How
wou
ld y
ou e
stim
ate
the
radi
us
of E
arth
bas
ed o
n E
rato
sth
enes
’es
tim
ate
of i
ts d
iam
eter
?S
amp
le a
nsw
er:
Use
a c
alcu
lato
r to
div
ide
46,2
50 k
m b
y 2�
.
Rea
din
g t
he
Less
on
1.N
ame
all
soli
ds f
rom
th
e fo
llow
ing
list
for
wh
ich
eac
h v
olu
me
form
ula
can
be
use
d:pr
ism
,pyr
amid
,con
e,cy
lin
der
,sph
ere,
hem
isph
ere.
a.V
�B
hp
rism
,cyl
ind
erb
.V�
�4 3� �r3
sph
ere
c.V
��1 3� B
hp
yram
id,c
on
ed
.V�
�r2
hcy
lind
er
e.V
��1 3� �
r2h
con
ef.
V�
�2 3� �r3
hem
isp
her
e
2.L
et r
repr
esen
t th
e ra
diu
s an
d d
repr
esen
t th
e di
amet
er o
f a
sph
ere.
Det
erm
ine
wh
eth
erea
ch f
orm
ula
bel
ow c
an b
e u
sed
to f
ind
the
volu
me
of a
sph
ere,
a h
emis
pher
e,or
nei
ther
.
a.V
��2�
3r3�
hem
isp
her
eb
.V�
�1 6� �d
3sp
her
e
c.V
��1 3� �
r3n
eith
erd
.V�
�3 4� �r3
nei
ther
e.V
��� 1d 23 �
hem
isp
her
ef.
V�
�4 3� �r2
hn
eith
er
3.C
ompa
re t
he
volu
mes
of
thes
e th
ree
soli
ds.T
hen
com
plet
e th
e se
nte
nce
bel
ow.
Of
the
thre
e so
lids
sh
own
abo
ve,t
he
has
th
e la
rges
t vo
lum
e an
d th
e
has
th
e sm
alle
st v
olu
me.
Hel
pin
g Y
ou
Rem
emb
er
4.A
goo
d w
ay t
o re
mem
ber
som
eth
ing
is t
o ex
plai
n i
t to
som
eon
e el
se.S
upp
ose
that
you
r cl
assm
ate
Lor
etta
kn
ows
that
th
e ex
pres
sion
s �4 3� �
r3an
d 4�
r2ar
e u
sed
in f
indi
ng
mea
sure
men
ts r
elat
ed t
o sp
her
es,b
ut
can
’t re
mem
ber
wh
ich
on
e is
use
d to
fin
d th
esu
rfac
e ar
ea o
f a
sph
ere
and
wh
ich
on
e is
use
d to
fin
d th
e vo
lum
e.H
ow c
an y
ou h
elp
her
to r
emem
ber
wh
ich
is
wh
ich
?S
amp
le a
nsw
er:
Lo
ok
at t
he
po
wer
s o
f r
in t
he
two
exp
ress
ion
s.T
he
exp
ress
ion
wit
h r
3w
ill g
ive
a m
easu
rem
ent
incu
bic
un
its,
so it
is t
he
exp
ress
ion
fo
r vo
lum
e.T
he
exp
ress
ion
wit
h r
2
will
giv
e a
mea
sure
men
t in
sq
uar
e u
nit
s,so
it is
th
e ex
pre
ssio
n f
or
surf
ace
area
.
con
esp
her
e
2r
r
rr
r
©G
lenc
oe/M
cGra
w-H
ill74
0G
lenc
oe G
eom
etry
Sp
her
es a
nd
Den
sity
Th
e d
ensi
tyof
a m
etal
is
a ra
tio
of i
ts m
ass
to i
ts v
olu
me.
For
exam
ple,
the
mas
s of
alu
min
um
is
2.7
gram
s pe
r cu
bic
cen
tim
eter
.H
ere
is a
lis
t of
sev
eral
met
als
and
thei
r de
nsi
ties
.
Alu
min
um
2.7
g/cm
3C
oppe
r8.
96 g
/cm
3
Gol
d19
.32
g/cm
3Ir
on7.
874
g/cm
3
Lea
d11
.35
g/cm
3P
lati
nu
m21
.45
g/cm
3
Sil
ver
10.5
0 g/
cm3
To
calc
ula
te t
he
mas
s of
a p
iece
of
met
al,m
ult
iply
vol
um
e by
den
sity
.
Fin
d t
he
mas
s of
a s
ilve
r b
all
that
is
0.8
cm
in d
iam
eter
.
M�
D
V
�10
.5
�4 3� �(0
.4)3
�10
.5 (
0.27
)�
2.83
Th
e m
ass
is a
bou
t 2.
83 g
ram
s.
Fin
d t
he
mas
s of
eac
h m
etal
bal
l d
escr
ibed
.Ass
um
e th
e b
alls
are
sp
her
ical
.Rou
nd
you
r an
swer
s to
th
e n
eare
st t
enth
.
1.a
copp
er b
all
1.2
cm i
n d
iam
eter
8.1
g
2.a
gold
bal
l 0.
6 cm
in
dia
met
er2.
2 g
3.an
alu
min
um
bal
l w
ith
rad
ius
3 cm
305.
4 g
4.a
plat
inu
m b
all
wit
h r
adiu
s 0.
7 cm
30.8
g
Sol
ve.A
ssu
me
the
bal
ls a
re s
ph
eric
al.R
oun
d y
our
answ
ers
to t
he
nea
rest
ten
th.
5.A
lea
d ba
ll w
eigh
s 32
6 g.
Fin
d th
e ra
diu
s of
th
e ba
ll t
o th
e n
eare
st
ten
th o
f a
cen
tim
eter
.1.
9 cm
6.A
n i
ron
bal
l w
eigh
s 80
4 g.
Fin
d th
e di
amet
er o
f th
e ba
ll t
o th
e n
eare
st t
enth
of
a ce
nti
met
er.
5.8
cm
7.A
sil
ver
ball
an
d a
copp
er b
all
each
hav
e a
diam
eter
of
3.5
cm.
Wh
ich
wei
ghs
mor
e? H
ow m
uch
mor
e?si
lver
;34
.6 g
8.A
n a
lum
inu
m b
all
and
a le
ad b
all
each
hav
e a
radi
us
of 1
.2 c
m.
Wh
ich
wei
ghs
mor
e? H
ow m
uch
mor
e?le
ad;
62.6
g
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-3
13-3
Exam
ple
Exam
ple
Answers (Lesson 13-3)
© Glencoe/McGraw-Hill A11 Glencoe Geometry
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Co
ng
ruen
t an
d S
imila
r S
olid
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-4
13-4
©G
lenc
oe/M
cGra
w-H
ill74
1G
lenc
oe G
eom
etry
Lesson 13-4
Co
ng
ruen
t o
r Si
mila
r So
lids
If t
he
corr
espo
ndi
ng
angl
es a
nd
side
s of
tw
o so
lids
are
con
gru
ent,
then
th
e so
lids
are
con
gru
ent.
Als
o,th
e co
rres
pon
din
g fa
ces
are
con
gru
ent
and
thei
r su
rfac
e ar
eas
and
volu
mes
are
equ
al.S
olid
s th
at h
ave
the
sam
e sh
ape
but
are
diff
eren
t si
zes
are
sim
ilar
.You
can
det
erm
ine
wh
eth
er t
wo
soli
ds a
re s
imil
ar b
y co
mpa
rin
gth
e ra
tio,
or s
cale
fac
tor,
of c
orre
spon
din
g li
nea
r m
easu
rem
ents
.
Des
crib
e ea
ch p
air
of s
olid
s.
•F
igu
res
I an
d II
are
sim
ilar
bec
ause
th
e fi
gure
s h
ave
the
sam
e sh
ape.
Th
e ra
tio
of e
ach
pair
of
corr
espo
ndi
ng
side
s is
1:3
.•
Fig
ure
s II
I an
d IV
are
con
gru
ent
beca
use
th
ey h
ave
the
sam
e sh
ape
and
all
corr
espo
ndi
ng
mea
sure
men
ts a
re t
he
sam
e.•
Fig
ure
s V
an
d V
I ar
e n
ot c
ongr
uen
t,an
d th
ey a
re n
ot s
imil
ar b
ecau
se �4 8�
�1 12 2�
.
Det
erm
ine
wh
eth
er e
ach
pai
r of
sol
ids
are
sim
ila
r,co
ng
ruen
t,or
nei
ther
.
1.2.
sim
ilar
nei
ther
3.4.
con
gru
ent
con
gru
ent
5.6.
nei
ther
sim
ilar
2 7
21
6
5
8
5
8
4
4
88
5
5
2
2
2 26
6
7
7
12
4
5
1
106
8
53
4
III
IIIIV
VV
Isi
mila
rco
ngru
ent
non-
sim
ilar
125
5
512
124
85
5
5
7
7
9
6
43
2
Exer
cises
Exer
cises
Exam
ple
Exam
ple
©G
lenc
oe/M
cGra
w-H
ill74
2G
lenc
oe G
eom
etry
Pro
per
ties
of
Sim
ilar
Solid
sT
hes
e tw
o so
lids
ar
e si
mil
ar w
ith
a s
cale
fac
tor
of 1
:2.T
he
surf
ace
area
s ar
e 62
cm
2an
d 24
8 cm
2an
d th
e vo
lum
es a
re
30 c
m3
and
240
cm3 .
Not
ice
that
th
e ra
tio
of t
he
surf
ace
area
s is
62
:248
,wh
ich
is
1:4
or 1
2:2
2 ,an
d th
e ra
tio
of t
he
volu
mes
is
30:2
40,w
hic
h i
s 1:
8 or
13:2
3 .
If tw
o so
lids
are
sim
ilar
with
a s
cale
fac
tor
of a
:b,
then
the
sur
face
ar
eas
have
a r
atio
of
a2:b
2 , a
nd t
he v
olum
es h
ave
a ra
tio o
f a
3:b
3 .
Use
th
e tw
o sp
her
es.
a.F
ind
th
e sc
ale
fact
or f
or t
he
two
sph
eres
.T
he
scal
e fa
ctor
for
th
e tw
o sp
her
es i
s th
e sa
me
as
the
rati
o of
th
eir
radi
i,or
5:3
.
b.
Fin
d t
he
rati
o of
th
e su
rfac
e ar
eas
of t
he
two
sph
eres
.T
he
rati
o of
th
e su
rfac
e ar
eas
is 5
2:3
2or
25:
9.
c.F
ind
th
e ra
tio
of t
he
volu
mes
of
the
two
sph
eres
.T
he
rati
o of
th
e vo
lum
es i
s 53
:33
or 1
25:2
7.
Fin
d t
he
scal
e fa
ctor
for
eac
h p
air
of s
imil
ar f
igu
res.
Th
en f
ind
th
e ra
tio
of t
hei
rsu
rfac
e ar
eas
and
th
e ra
tio
of t
hei
r vo
lum
es.
1.2.
3:4;
9:16
;27
:64
7:4;
49:1
6;34
3:64
3.4.
4:5;
16:2
5;64
:125
2:1;
4:1;
8:1
5.6.
5:4;
25:1
6;12
5:64
1:2:
1:4;
1:8
86
5
3
1215
4 yd
16 y
d
15 m
12 m
7 in
.4
in.
3 ft
4 ft
5 cm
3 cm
10 c
m5
cm2
cm3 cm
6 cm
4 cm
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Co
ng
ruen
t an
d S
imila
r S
olid
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-4
13-4
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 13-4)
© Glencoe/McGraw-Hill A12 Glencoe Geometry
Skil
ls P
ract
ice
Co
ng
ruen
t an
d S
imila
r S
olid
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-4
13-4
©G
lenc
oe/M
cGra
w-H
ill74
3G
lenc
oe G
eom
etry
Lesson 13-4
Det
erm
ine
wh
eth
er e
ach
pai
r of
sol
ids
are
sim
ila
r,co
ng
ruen
t,or
nei
ther
.
1.si
mila
r
2.n
eith
er
3.si
mila
r
4.co
ng
ruen
t
For
Exe
rcis
es 5
–8,r
efer
to
the
two
sim
ilar
pri
sms.
5.F
ind
the
scal
e fa
ctor
of
the
two
pris
ms.
�3 2�
6.F
ind
the
rati
o of
th
e su
rfac
e ar
eas.
�9 4�
7.F
ind
the
rati
o of
th
e vo
lum
es.
�2 87 �
8.S
upp
ose
the
volu
me
of t
he
larg
er p
rism
is
810
cubi
c ce
nti
met
ers.
Fin
d th
e vo
lum
e of
th
esm
alle
r pr
ism
.
240
cm3
15 c
m12
cm
9 cm
10 c
m8
cm6
cm
18 in
.
16 in
.16
in.
9 in
.
6 m
m
6 m
m
4 m
m9
mm
12 ft
12 ft
14 ft
20 ft
20 ft
21 ft
20 c
m20
cm
10 c
m
4 cm
40 c
m
8 cm
©G
lenc
oe/M
cGra
w-H
ill74
4G
lenc
oe G
eom
etry
Det
erm
ine
wh
eth
er e
ach
pai
r of
sol
ids
are
sim
ila
r,co
ng
ruen
t,or
nei
ther
.
1.co
ng
ruen
t
2.si
mila
r
3.n
eith
er
4.si
mila
r
For
Exe
rcis
es 5
–8,r
efer
to
the
two
sim
ilar
pri
sms.
5.F
ind
the
scal
e fa
ctor
of
the
two
pris
ms.
�5 3�
6.F
ind
the
rati
o of
th
e su
rfac
e ar
eas.
�2 95 �
7.F
ind
the
rati
o of
th
e vo
lum
es.
�1 22 75 �
8.S
upp
ose
the
surf
ace
area
of
the
larg
er p
rism
is
2560
squ
are
met
ers.
Fin
d th
e su
rfac
ear
ea o
f th
e sm
alle
r pr
ism
.92
1.6
m2
9.M
INIA
TUR
ESF
ran
k L
loyd
Wri
ght
desi
gned
eve
ry a
spec
t of
th
e Im
peri
al H
otel
in
Tok
yo,
incl
udin
g th
e ch
airs
.The
dim
ensi
ons
of a
min
iatu
re I
mpe
rial
Hot
el c
hair
are
6.2
5 in
ches
�3
inch
es �
2.5
inch
es.I
f th
e sc
ale
of t
he
repl
ica
is 1
:6,w
hat
are
th
e di
men
sion
s of
th
eor
igin
al c
hai
r?
37.5
in.�
18 in
.�15
in.
20 m
20 m
22 m
12 m
12 m
13.2
m
7.5
cm
20 c
m
15 c
m
4.5
cm
12 c
m9
cm
18 ft
24 ft
24 ft
9 ft
12 m
12 m
15 m
2.5
m
2 m
9.6
m
25 in
.15 in
.
30 in
.20
in.
Pra
ctic
e (
Ave
rag
e)
Co
ng
ruen
t an
d S
imila
r S
olid
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-4
13-4
Answers (Lesson 13-4)
© Glencoe/McGraw-Hill A13 Glencoe Geometry
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csC
on
gru
ent
and
Sim
ilar
So
lids
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-4
13-4
©G
lenc
oe/M
cGra
w-H
ill74
5G
lenc
oe G
eom
etry
Lesson 13-4
Pre-
Act
ivit
yH
ow a
re s
imil
ar s
olid
s ap
pli
ed t
o m
inia
ture
col
lect
ible
s?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 13
-4 a
t th
e to
p of
pag
e 70
7 in
you
r te
xtbo
ok.
If y
ou w
ant
to m
ake
a m
inia
ture
wit
h a
sca
le f
acto
r of
1:6
4,h
ow c
an y
ouu
se t
he
actu
al o
bjec
t to
fin
d th
e m
easu
rem
ents
you
sh
ould
use
to
con
stru
ctth
e m
inia
ture
?S
amp
le a
nsw
er:T
ake
linea
r m
easu
rem
ents
of
the
actu
al o
bje
ct.D
ivid
e ea
ch m
easu
rem
ent
by 6
4 to
fin
d t
he
corr
esp
on
din
g m
easu
rem
ent
for
the
min
iatu
re.
Rea
din
g t
he
Less
on
1.D
eter
min
e w
het
her
eac
h s
tate
men
t is
alw
ays,
som
etim
es,o
r n
ever
tru
e.a.
Tw
o cu
bes
are
sim
ilar
.al
way
sb
.T
wo
con
es a
re s
imil
ar.
som
etim
esc.
Tw
o cy
lin
ders
in
wh
ich
th
e h
eigh
t is
tw
ice
the
diam
eter
are
sim
ilar
.al
way
sd
.T
wo
cyli
nde
rs w
ith
th
e sa
me
volu
me
are
con
gru
ent.
som
etim
ese.
A p
rism
wit
h a
squ
are
base
an
d a
squ
are
pyra
mid
are
sim
ilar
.n
ever
f.T
wo
rect
angu
lar
pris
ms
wit
h e
qual
su
rfac
e ar
eas
are
sim
ilar
.so
met
imes
g.N
onsi
mil
ar s
olid
s h
ave
diff
eren
t vo
lum
es.
som
etim
esh
.T
wo
hem
isph
eres
wit
h t
he
sam
e ra
diu
s ar
e co
ngr
uen
t.al
way
s
2.S
upp
ly t
he
mis
sin
g ra
tios
.
a.If
th
e ra
tio
of t
he
diam
eter
s of
tw
o sp
her
es i
s 3:
1,th
en t
he
rati
o of
th
eir
surf
ace
area
s
is
,an
d th
e ra
tio
of t
hei
r vo
lum
es i
s .
b.
If t
he
rati
o of
th
e ra
dii
of t
wo
hem
isph
eres
is
2:5,
then
th
e ra
tio
of t
hei
r su
rfac
e ar
eas
is
,an
d th
e ra
tio
of t
hei
r vo
lum
es i
s .
c.If
tw
o co
nes
are
sim
ilar
an
d th
e ra
tio
of t
hei
r h
eigh
ts i
s �4 3� ,
then
th
e ra
tio
of t
hei
r
volu
mes
is
,an
d th
e ra
tio
of t
hei
r su
rfac
e ar
eas
is
.
d.
If t
wo
cyli
nde
rs a
re s
imil
ar a
nd
the
rati
o of
th
eir
surf
ace
area
s is
100
:49,
then
th
e
rati
o of
th
e ra
dii
of t
hei
r ba
ses
is
,an
d th
e ra
tio
of t
hei
r vo
lum
es i
s
.
Hel
pin
g Y
ou
Rem
emb
er3.
A g
ood
way
to
rem
embe
r a
new
mat
hem
atic
al c
once
pt i
s to
rel
ate
it t
o so
met
hin
g yo
ual
read
y kn
ow.H
ow c
an w
hat
you
kn
ow a
bou
t th
e u
nit
s u
sed
to m
easu
re l
engt
hs,
area
s,an
d vo
lum
es h
elp
you
to
rem
embe
r th
e th
eore
m a
bou
t th
e ra
tios
of
surf
ace
area
s an
dvo
lum
es o
f si
mil
ar s
olid
s?S
amp
le a
nsw
er:
Len
gth
s ar
e m
easu
red
in li
nea
ru
nit
s,su
rfac
e ar
eas
in s
qu
are
un
its,
and
vo
lum
es in
cu
bic
un
its.
Take
th
esc
ale
fact
or,
wh
ich
is t
he
rati
o o
f lin
ear
mea
sure
men
ts in
th
e so
lids,
and
squ
are
it t
o g
et t
he
rati
o o
f th
eir
surf
ace
area
s o
r cu
be
it t
o g
et t
he
rati
oo
f th
eir
volu
mes
.
1000
:343
10:7
�1 96 ��6 24 7�
8:12
54:
25
27:1
9:1
©G
lenc
oe/M
cGra
w-H
ill74
6G
lenc
oe G
eom
etry
Co
ng
ruen
t an
d S
imila
r S
olid
s
Det
erm
ine
wh
eth
er e
ach
pai
r of
sol
ids
is s
imil
ar,
con
gru
ent,
or n
eith
er.
1.2.
nei
ther
sim
ilar
3.4.
con
gru
ent
sim
ilar
Th
e tw
o re
ctan
gula
r p
rism
s sh
own
at
the
righ
t ar
e si
mil
ar.
5.F
ind
the
rati
o of
th
e pe
rim
eter
s of
th
e ba
ses.
7:5
6.W
hat
is
the
rati
o of
th
e su
rfac
e ar
eas?
72:5
2o
r 49
:25
7.S
upp
ose
the
volu
me
of t
he
smal
ler
pris
m i
s 60
in
3 .F
ind
the
volu
me
of t
he
larg
er p
rism
.16
4.64
in3
Det
erm
ine
wh
eth
er e
ach
sta
tem
ent
is t
rue
or f
als
e.If
th
e st
atem
ent
is f
alse
,rew
rite
it
so t
hat
it
is t
rue.
8.If
tw
o cy
lin
ders
are
sim
ilar
,th
en t
hei
r vo
lum
es a
re e
qual
.Fa
lse;
if t
wo
cyl
ind
ers
are
con
gru
ent,
then
th
eir
volu
mes
are
eq
ual
.
9.D
oubl
ing
the
hei
ght
of a
cyl
inde
r do
ubl
es t
he
volu
me.
tru
e
10.T
wo
soli
ds a
re c
ongr
uen
t if
th
ey h
ave
the
sam
e sh
ape.
Fals
e;tw
o s
olid
s ar
e si
mila
r if
th
ey h
ave
the
sam
e sh
ape.
7 in
.5
in.
24 y
d
12 y
d
12 y
d6
yd 8 yd
16 y
d12
m
3 m
3 m
3 m
3 m
3 m
3 m
4 m
4 m
4 m
4 m
4 m
10 m
48 m
16 m15
m
14 c
m
11 c
m
7 cm
7 cm
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-4
13-4
Answers (Lesson 13-4)
© Glencoe/McGraw-Hill A14 Glencoe Geometry
Stu
dy G
uid
e a
nd I
nte
rven
tion
Co
ord
inat
es in
Sp
ace
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-5
13-5
©G
lenc
oe/M
cGra
w-H
ill74
7G
lenc
oe G
eom
etry
Lesson 13-5
Gra
ph
So
lids
in S
pac
eIn
spa
ce,y
ou c
an d
escr
ibe
the
loca
tion
of
a po
int
usi
ng
an o
rder
ed t
rip
leof
rea
ln
um
bers
.Th
e x-
,y-,
and
z-ax
es a
re p
erpe
ndi
cula
r to
ea
ch o
ther
,an
d th
e co
ordi
nat
es f
or p
oin
t P
are
the
orde
red
trip
le (
�4,
6,5)
.A r
ecta
ngu
lar
pris
m c
an b
edr
awn
to
show
per
spec
tive
.
Gra
ph
th
e re
ctan
gula
r so
lid
th
at
con
tain
s th
e or
der
ed t
rip
le (
2,1,
�2)
an
d t
he
orig
in.L
abel
th
e co
ord
inat
es o
f ea
ch v
erte
x.•
Plo
t th
e x-
coor
din
ate
firs
t.D
raw
a s
olid
seg
men
t fr
om t
he
orig
in 2
un
its
in t
he
posi
tive
dir
ecti
on.
•P
lot
the
y-co
ordi
nat
e n
ext.
Dra
w a
sol
id s
egm
ent
1 u
nit
in
th
e po
siti
ve d
irec
tion
.•
Plo
t th
e z-
coor
din
ate
nex
t.D
raw
a s
olid
seg
men
t 2
un
its
in t
he
neg
ativ
e di
rect
ion
.•
Dra
w t
he
rect
angu
lar
pris
m,u
sin
g do
tted
lin
es f
or
hid
den
edg
es o
f th
e pr
ism
.•
Lab
el t
he
coor
din
ates
of
each
ver
tex.
Gra
ph
th
e re
ctan
gula
r so
lid
th
at c
onta
ins
the
give
n p
oin
t an
d t
he
orig
in a
sve
rtic
es.L
abel
th
e co
ord
inat
es o
f ea
ch v
erte
x.
1.A
(2,1
,3)
2.G
(�1,
2,3)
3.P
(�2,
1,�
1)4.
T(�
1,3,
2)
y
x
z
( 0, 0
, 0)
( 0, 3
, 0)
( �1,
3, 0
)
( 0, 0
, 2)
( 0, 3
, 2)
( �1,
0, 2
)
( �1,
0, 0
)
T( �
1, 3
, 2)
y
x
z
( 0, 0
, 0)
( 0, 1
, 0)
P( �
2, 1
, �1)
( �2,
0, �
1)( �
2, 1
, 0)
( �2,
0, 0
)
( 0, 0
, �1)
( 0, 1
, �1)
y
x
z
( 0, 0
, 0)
( 0, 0
, 3)
( �1,
2, 0
)( �
1, 0
, 0)
( �1,
0, 3
)G
( �1,
2, 3
)
( 0, 2
, 0)
( 0, 2
, 3)
y
x
z( 0
, 0, 3
)
( 0, 0
, 0)
( 2, 0
, 3)
( 2, 0
, 0)
( 2, 1
, 0)
( 0, 1
, 0)
( 0, 1
, 3)
A( 2
, 1, 3
)
y
x
z
( 0, 0
, 0)
( 0, 1
, 0)
( 0, 1
, �2)
( 2, 1
, �2)
( 2, 0
, �2)
( 0, 0
, �2)
( 2, 0
, 0)
( 2, 1
, 0)
y
x
z O
P( �
4, 6
, 5)
Exer
cises
Exer
cises
Exam
ple
Exam
ple
©G
lenc
oe/M
cGra
w-H
ill74
8G
lenc
oe G
eom
etry
Dis
tan
ce a
nd
Mid
po
int
Form
ula
sYo
u c
an e
xten
d th
e D
ista
nce
For
mu
la a
nd
the
Mid
poin
t F
orm
ula
to
thre
e di
men
sion
s to
fin
d th
e di
stan
ce b
etw
een
tw
o po
ints
in
spa
ce
and
to f
ind
the
mid
poin
t of
th
e se
gmen
t co
nn
ecti
ng
two
poin
ts.
Dis
tan
ce F
orm
ula
Giv
en t
wo
poin
ts A
(x1,
y1,
z1)
and
B(x
2, y
2, z
2) in
spa
ce,
the
dist
ance
bet
wee
n
in S
pac
eA
and
Bis
giv
en b
y A
B�
�(x
1�
�x 2
)2�
�(y
1�
�y 2
)2�
�(z
1�
�z 2
)2�
.
Mid
po
int
Fo
rmu
laG
iven
tw
o po
ints
A(x
1, y
1, z
1) a
nd B
(x2,
y2,
z2)
in s
pace
, th
e m
idpo
int
of A�
B�is
in S
pac
eat
��x 1� 2
x 2�
, �y 1
� 2y 2
�, �z 1
� 2z 2
��.
Det
erm
ine
the
dis
tan
ce b
etw
een
A(3
,2,�
5) a
nd
B(�
4,6,
9).
Th
en d
eter
min
e th
e co
ord
inat
es o
f th
e m
idp
oin
t of
A �B�
.
AB
��
(x1
��
x 2)2
��
(y1
��
y 2)2
��
(z1
��
z 2)2
��
�(3
�(
��
4))2
��
(2 �
�6)
2�
�(�
5 �
�9)
2�
��
72�
(�
�4)
2�
�(�
14�
)2 ��
�49
��
16 �
�19
6�
�16
.2
mid
poin
t of
A�B�
���x 1
� 2x 2
�,�
y 1� 2
y 2�
,�z 1
� 2z 2
��
���3
�
2(�4)
�,�
2� 2
6�
,��
5 2�9
��
�(�
0.5,
4,2)
Det
erm
ine
the
dis
tan
ce b
etw
een
eac
h p
air
of p
oin
ts.T
hen
det
erm
ine
the
coor
din
ates
of
the
mid
poi
nt
Mof
th
e se
gmen
t jo
inin
g th
e p
air
of p
oin
ts.
1.A
(0,7
,�4)
an
d B
(�2,
8,3)
2.C
(�7,
6,5)
an
d D
(10,
2,�
5)
AB
��
54��
7.3
;M
��1,
�1 25 �,�
�1 2� �C
D�
�40
5�
�20
.1;
M��3 2� ,
4,0 �
3.E
(3,1
,�2)
an
d F
(�2,
3,4)
4.G
(�4,
1,1)
an
d H
(0,2
,�1)
EF
��
65��
8.1
;M
��1 2� ,2,
1 �G
H�
�21�
�4.
6;M
��2,
�3 2� ,0 �
5.J
(6,1
,�2)
an
d K
(�1,
�2,
1)6.
L(�
5,0,
�3)
an
d N
(0,0
,�4)
JK�
�67�
�8.
2 ;
M��5 2� ,
��1 2� ,
��1 2� �
LN
��
26��
5.1;
M��
�5 2� ,0,
��7 2� �
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Co
ord
inat
es in
Sp
ace
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-5
13-5
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 13-5)
© Glencoe/McGraw-Hill A15 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Co
ord
inat
es in
Sp
ace
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-5
13-5
©G
lenc
oe/M
cGra
w-H
ill74
9G
lenc
oe G
eom
etry
Lesson 13-5
Gra
ph
th
e re
ctan
gula
r so
lid
th
at c
onta
ins
the
give
n p
oin
t an
d t
he
orig
in a
sve
rtic
es.L
abel
th
e co
ord
inat
es o
f ea
ch v
erte
x.
1.A
(�5,
3,2)
2.H
(3,2
,5)
3.D
ilat
e th
e pr
ism
by
a sc
ale
fact
or o
f 2.
Gra
ph t
he
imag
e u
nde
r th
e di
lati
on.
A�(
�4,
6,2)
,B�(
�4,
0,2)
,C�(
0,0,
2),D
�(0,
6,2)
,E
�(�
4,6,
0),F
�(�
4,0,
0),G
�(0,
0,0)
,H�(
0,6,
0)
Det
erm
ine
the
dis
tan
ce b
etw
een
eac
h p
air
of p
oin
ts.T
hen
det
erm
ine
the
coor
din
ates
of
the
mid
poi
nt
Mof
th
e se
gmen
t jo
inin
g th
e p
air
of p
oin
ts.
4.R
(2,1
,0)
and
S(3
,3,4
)5.
Q(5
,0,�
2) a
nd
T(2
,3,2
)
RS
��
21�;��5 2� ,
2,2 �
QT
��
34�;��7 2� ,
�3 2� ,0 �
6.A
(�4,
1,6)
an
d B
(�1,
0,4)
7.J
(0,5
,1)
and
K(4
,�3,
2)
AB
��
14�;��
�5 2� ,�1 2� ,
5 �JK
�9;
�2,1,
�3 2� �
y
x
z
A�
B�
C�
D�
E�
F�
G�
H�
y
x
z
AB
C
GH
ED
F
y
x
z
N( 0
, 0, 0
)
M( 3
, 0, 0
)L
( 3, 2
, 0)
P( 0
, 2, 0
)
K( 0
, 2, 5
)J(
0, 0
, 5)
I(3,
0, 5
)
H( 3
, 2, 5
)
y
x
zA
( �5,
3, 2
)
E( �
5, 3
, 0)
B( �
5, 0
, 2)
C( 0
, 0, 2
)D
( 0, 3
, 2)
H( 0
, 3, 0
)
G( 0
, 0, 0
)
F( �
5, 0
, 0)
©G
lenc
oe/M
cGra
w-H
ill75
0G
lenc
oe G
eom
etry
Gra
ph
th
e re
ctan
gula
r so
lid
th
at c
onta
ins
the
give
n p
oin
t an
d t
he
orig
in a
sve
rtic
es.L
abel
th
e co
ord
inat
es o
f ea
ch v
erte
x.
1.E
(4,6
,�2)
2.R
(�3,
�5,
4)
Det
erm
ine
the
dis
tan
ce b
etw
een
eac
h p
air
of p
oin
ts.T
hen
det
erm
ine
the
coor
din
ates
of
the
mid
poi
nt
Mof
th
e se
gmen
t jo
inin
g th
e p
air
of p
oin
ts.
3.Y
(�5,
1,2)
an
d Z
(3,�
3,1)
4.E
(4,2
,0)
and
F(3
,2,�
2)
YZ
�9;
��1,
�1,
�3 2� �E
F�
�5�;
��7 2� ,2,
�1 �
5.B
(�2,
�2,
�3)
an
d C
(1,�
3,0)
6.H
(2,0
,�3)
an
d I(
4,�
1,5)
BC
��
19�;��
�1 2� ,�
�5 2� ,�
�3 2� �H
I��
69�;�3,
��1 2� ,
1 �
7.A
NIM
ATI
ON
Der
ek w
ants
to
anim
ate
an i
mag
e fo
r h
is s
cien
ce p
rese
nta
tion
by
mov
ing
it f
rom
on
e po
siti
on t
o an
oth
er.T
he
mes
h o
f th
e im
age
is a
rec
tan
gula
r pr
ism
wit
hco
ordi
nate
s A
(�3,
2,3)
,B(�
3,0,
3),C
(0,0
,3),
D(0
,2,3
),E
(�3,
2,0)
,F(�
3,0,
0),G
(0,0
,0),
and
H(0
,2,0
).F
ind
the
coor
dina
tes
of t
he m
esh
afte
r th
e tr
ansl
atio
n (x
,y,z
) →
(x�
7,y,
z).
Gra
ph b
oth
th
e pr
eim
age
and
imag
e of
th
e m
esh
.A
�(�
10,2
,3),
B�(
�10
,0,3
),C
�(�
7,0,
3),
D�(
�7,
2,3)
,E�(
�10
,2,0
),F
�(�
10,0
,0),
G�(
�7,
0,0)
,H�(
�7,
2,0)
y
x
zA
�B
�
C�
D�
E�
F�
G�
H�
AB
CD
EF
GH
y
x
z
X( 0
, 0, 0
)
Y( 0
, �5,
0)
V( �
3, �
5, 0
)R( �
3, �
5, 4
)S
( �3,
0, 4
)
T( 0
, 0, 4
)U
( 0, �
5, 4
)
W( �
3, 0
, 0)
y
x
z
K( 0
, 0, 0
)
J(4,
0, 0
)I(
4, 6
, 0)
L( 0
, 6, 0
)
H( 0
, 6, �
2)
E( 4
, 6, �
2)F
( 4, 0
, �2)
G( 0
, 0, �
2)
Pra
ctic
e (
Ave
rag
e)
Co
ord
inat
es in
Sp
ace
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-5
13-5
Answers (Lesson 13-5)
© Glencoe/McGraw-Hill A16 Glencoe Geometry
Readin
g t
o L
earn
Math
em
ati
csC
oo
rdin
ates
in S
pac
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-5
13-5
©G
lenc
oe/M
cGra
w-H
ill75
1G
lenc
oe G
eom
etry
Lesson 13-5
Pre-
Act
ivit
yH
ow i
s th
ree-
dim
ensi
onal
gra
ph
ing
use
d i
n c
omp
ute
r an
imat
ion
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 13
-5 a
t th
e to
p of
pag
e 71
4 in
you
r te
xtbo
ok.
Wh
y w
ould
a m
esh
be
crea
ted
firs
t?S
amp
le a
nsw
er:
A m
esh
is a
no
utl
ine
that
th
e an
imat
or
wo
uld
use
fir
st li
ke a
ske
tch
bef
ore
ren
der
ing
a f
inal
imag
e.
Rea
din
g t
he
Less
on
1.R
efer
to
the
figu
re.M
atch
eac
h p
oin
t fr
om t
he
firs
t co
lum
n
wit
h i
ts c
oord
inat
es f
rom
th
e se
con
d co
lum
n.
a.A
iiii.
(3,0
,0)
b.
Bvi
ii.(
3,0,
�4)
c.O
vii
i.(3
,�2,
0)
d.
Ji
iv.
(3,�
2,�
4)
e.H
ivv.
(0,0
,0)
f.K
iivi
.(0,
�2,
0)
g.T
viii
vii.
(0,�
2,�
4)
h.
Rvi
ivi
ii.(
0,0,
�4)
2.W
hic
h o
f th
e fo
llow
ing
expr
essi
ons
give
th
e di
stan
ce b
etw
een
th
e po
ints
at
(4,�
1,�
5)an
d (�
3,2,
�9)
?A
,E,H
A.
�72
�(
��
3)2
��
42 �B
.�12
�1
�2
�(�
�14
)2�
C.
�22
�2
�2
�42
�D
. ��1 2� ,�1 2� ,
�7 �
E.
�(�
3 �
�4)
2�
�(�
1 �
�2)
2�
�(�
9 �
�5)
2�
F.�
24�
G.�
(�3
��
4)2
��
[2 �
�(�
1)]2
��
[��
9 �
(��
5)]2
�H
.�74�
Hel
pin
g Y
ou
Rem
emb
er
3.A
goo
d w
ay t
o re
mem
ber
new
mat
hem
atic
al f
orm
ula
s is
to
rela
te t
hem
to
ones
you
alre
ady
know
.How
can
you
use
you
r kn
owle
dge
of t
he
Dis
tan
ce a
nd
Mid
poin
t F
orm
ula
sin
tw
o di
men
sion
s to
rem
embe
r th
e fo
rmu
las
in t
hre
e di
men
sion
s?S
amp
le a
nsw
er:
Sta
rt w
ith
th
e fo
rmu
las
for
two
dim
ensi
on
s.A
dd
a t
hir
d t
erm
un
der
th
era
dic
al in
th
e D
ista
nce
Fo
rmu
la a
nd
a t
hir
d c
oo
rdin
ate
in t
he
Mid
po
int
Fo
rmu
la t
hat
is ju
st li
ke t
he
oth
er t
wo
exc
ept
that
th
e va
riab
le is
zra
ther
than
xo
r y.
y
x
z
A
KBO
R
H
T
J
©G
lenc
oe/M
cGra
w-H
ill75
2G
lenc
oe G
eom
etry
Pla
nes
an
d C
ylin
dri
cal S
urf
aces
Con
side
r th
e po
ints
(x,
y,z)
in
spa
ce w
hos
e co
ordi
nat
es s
atis
fy t
he
equ
atio
n z
�1.
Sin
ce x
an
dy
do n
ot o
ccu
r in
th
e eq
uat
ion
,an
y po
int
wit
h i
ts z
-coo
rdin
ate
equ
al t
o 1
has
coo
rdin
ates
th
at s
atis
fy t
he
equ
atio
n.T
hes
e ar
e th
e po
ints
in
th
e pl
ane
1 u
nit
abo
ve t
he
xy-p
lan
e.T
his
pl
ane
is p
erpe
ndi
cula
r to
th
e z-
axis
at
(0,0
,1).
Nex
t co
nsi
der
the
poin
ts (
x,y,
z) w
hos
e co
ordi
nat
es s
atis
fy x
2�
y2�
16.I
n t
he
xy-p
lan
e,al
l po
ints
on
th
e ci
rcle
wit
h c
ente
r (0
,0,0
) an
dra
diu
s 4
hav
e co
ordi
nat
es t
hat
sat
isfy
th
e eq
uat
ion
.In
th
e pl
ane
perp
endi
cula
r to
th
e z-
axis
at
(0,0
,k),
the
poin
ts t
hat
sat
isfy
th
eeq
uat
ion
are
th
ose
on t
he
circ
le w
ith
cen
ter
(0,0
,k)
and
radi
us
4.T
he
grap
h i
n s
pace
of
x2�
y2�
16 i
s an
in
fin
ite
cyli
ndr
ical
su
rfac
e w
hos
e ax
is i
s th
e z-
axis
an
d w
hos
e ra
diu
s is
4.
Des
crib
e th
e gr
aph
in
sp
ace
of e
ach
eq
uat
ion
.You
may
fin
d i
t h
elp
ful
to m
ake
sket
ches
on
a s
epar
ate
shee
t.
1.x
�5
the
pla
ne
per
pen
dic
ula
r to
th
e x-
axis
at
(5,0
,0)
2.y
��
2th
e p
lan
e p
erp
end
icu
lar
to t
he
y-ax
is a
t (0
,�2,
0)
3.x
�y
�7
the
pla
ne
par
alle
l to
th
e z-
axis
an
d c
on
tain
ing
th
e lin
e th
rou
gh
(0,7
,0)
and
(7,
0,0)
4.z2
�y2
�25
the
infi
nit
e cy
lind
rica
l su
rfac
e w
ho
se a
xis
is t
he
x-ax
is a
nd
wh
ose
rad
ius
is 5
5.(x
�2)
2�
(y�
5)2
�1
the
infin
ite c
ylin
dri
cals
urf
ace
wh
ose
axi
s is
th
e lin
ep
aral
lel t
o t
he
z-ax
is a
nd
pas
sin
g t
hro
ug
h (
2,5,
0) a
nd
wh
ose
rad
ius
is 1
6.x2
�y2
�z2
�0
the
po
int
(0,0
,0)
z
y
x
O
(0, 0
, k)
plan
e fo
r z �
k
z
y
x
O
(0, 0
, 1)
N
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
13-5
13-5
Answers (Lesson 13-5)
© Glencoe/McGraw-Hill A17 Glencoe Geometry
Chapter 13 Assessment Answer Key Form 1 Form 2APage 753 Page 754 Page 755
(continued on the next page)
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
A
B
D
C
C
A
B
D
A
B
B
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
B
D
B
D
B
D
A
D
C
a cylinder with a3-cm radius
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
C
C
A
C
C
D
B
B
A
D
A
© Glencoe/McGraw-Hill A18 Glencoe Geometry
Chapter 13 Assessment Answer KeyForm 2A (continued) Form 2BPage 756 Page 757 Page 758
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
C
D
B
C
D
A
D
D
B
32.4 in3
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
D
C
C
A
D
B
D
B
B
B
A
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
B
A
C
B
D
D
A
C
A
326.7 cm3
© Glencoe/McGraw-Hill A19 Glencoe Geometry
Chapter 13 Assessment Answer KeyForm 2CPage 759 Page 760
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
432 in3
2 ft
7690.6 ft3
1885.0 in3
270�3� ft3
7.2 in.
18 times
103.2 ft3
208.8 in3
2145 in3
1393.0 in3
968.7 cm3
13.
14.
15.
16.
17.
18.
19.
20.
B:
always
neither
612.5 m2
4:9
D�(15, �5, �3)
(1, 5, 7)
3�2�
314.2 in3
y
x
z
A
© Glencoe/McGraw-Hill A20 Glencoe Geometry
Chapter 13 Assessment Answer KeyForm 2DPage 761 Page 762
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
144 cm3
576 in3
923.6 cm3
3 cm
2057 in3
36 in2
12 times
100.5 cm3
106.4 cm3
7238 ft3
113.1 in3
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
38.7 in3
always
similar
1562.5 ft3
512:729
X�(�28, 8, 20)
14 units
(�8, 6, 4)
��14
�, �241�, ��
121��
y
x
z
A
© Glencoe/McGraw-Hill A21 Glencoe Geometry
Chapter 13 Assessment Answer KeyForm 3Page 763 Page 764
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
125 m3
184 cm3
114�3� in3
8 m
No, it willoverflow.
148.4 in3 � 96 in3
212.1 cm3
266.9 cm3
121.5 in3
263.9 in3
138.2 cm3
75,266.3 cm3
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
64 times
Yes; �32
3�� � 12�.
similar
1:3�4�
45 in.
C(3, �9, 10)
�14� units
118.0 mi
7104 mL
y
x
z
© Glencoe/McGraw-Hill A22 Glencoe Geometry
Chapter 13 Assessment Answer KeyPage 765, Open-Ended Assessment
Scoring Rubric
Score General Description Specific Criteria
• Shows thorough understanding of the concepts ofcongruent solids, similar solids, volume, ratios of surfaceareas and volumes, ordered triples, graphing points inspace, midpoints, and distances in three dimensions.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Figures and graphs are accurate and appropriate.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts of congruentsolids, similar solids, volume, ratios of surface areas andvolumes, ordered triples, graphing points in space,midpoints, and distances in three dimensions.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Figures and graphs are mostly accurate and appropriate.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts ofcongruent solids, similar solids, volume, ratios of surfaceareas and volumes, ordered triples, graphing points inspace, midpoints, and distances in three dimensions.
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Figures and graphs are mostly accurate.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work shown to substantiate the
final computation.• Figures and graphs may be accurate but lack detail or
explanation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of most of the concepts ofcongruent solids, similar solids, volume, ratios of surfaceareas and volumes, ordered triples, graphing points inspace, midpoints, and distances in three dimensions.
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Figures and graphs are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
© Glencoe/McGraw-Hill A23 Glencoe Geometry
An
swer
s
Chapter 13 Assessment Answer KeyPage 765, Open-Ended Assessment
Sample Answers
1. Sample coordinates:A(8, 0, 0), B(8, 16, 0), C(0, 16, 0),D(0, 0, 0), E(8, 0, 12), F(8, 16, 12),G(0, 16, 12), H(0, 0, 12);A�(2, 0, 0), B�(2, 4, 0), C�(0, 4, 0),D�(0, 0, 0), E�(2, 0, 3), F �(2, 4, 3),G�(0, 4, 3), H�(0, 0, 3)
2. The volume of the cylinder is �r2 � 2r.
The volume of the hemisphere is �2�3r3�.
The volume of the cone is �r2 � �3r
�.
Therefore, the total volume is
2�r3 � �2�
3r3� � �
�3r3� or 3�r3.
3. The first cylinder could have a radius of 3,a height of 4, a volume of 36�, and asurface area of 42�. The second cylindercould have a radius of 1, a height of 30, avolume of 30�, and a surface area of 62�.
4.
The volume of the pyramid is �163� 12� or
64 cubic units and the volume of theprism is 4 � 4 � 4 or 64 cubic units.
5. The formula for the volume of a prism isV � Bh. Since the base of a cylinder is acircle, its area is �r2. If you substitute�r2 for B in the V � Bh formula, youobtain V � �r2h for the volume of acylinder.
6. A sample pair of points are A(2, 3, 4) andC(4, 5, 6). Accept any pair of coordinatesA(x1, y1, z1) and A(x2, y2, z2) in which x1 � x2 � 6, y1 � y2 � 8, and z1 � z2 � 10.
4 in.4 in.4 in.
12 in.
4 in.
4 in.
y
x
z
44
4
In addition to the scoring rubric found on page A22, the following sample answers may be used as guidance in evaluating open-ended assessment items.
© Glencoe/McGraw-Hill A24 Glencoe Geometry
Chapter 13 Assessment Answer KeyVocabulary Test/Review Quiz 1 Quiz 3Page 766 Page 767 Page 768
Quiz 2Page 767
Quiz 4Page 768
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
false,similar solids
false,congruent solids
false,ordered triple
true
false, V � ��r
3
2h�
false, V � �4�
3r 3�
true
true
false, V � �r 2h
true
a3:b3
��x1 �
2x2�, �
y1 �
2y2�, �
z1 �
2z2��
1.
2.
3.
4.
5.
1152 ft3
2 cm
2827.4 in3
156 cm3
1005.3 cm3
1.
2.
3.
4.
5.
8 times
261.8 cm3
904.8 mm3
160.1 mm3
C
1.
2.
3.
4.
5.
neither
congruent
4:9
0.84 in.
false
1.
2.
3.
4.
5.
A�(5, �3, 5),B�(6, �2, 5),C�(2, �1, 5),D�(5, �2, 8)
�2, �52
�, �129��
�74�
C(14, �2, 11)
y
x
z
B
© Glencoe/McGraw-Hill A25 Glencoe Geometry
Chapter 13 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 769 Page 770
An
swer
s
Part I
Part II
6.
7.
8.
9.
10.
6.4 cm3
960 cm3
7.5 in3
1150.3 cm3
32�3� in3
1.
2.
3.
4.
5.
A
D
C
B
B
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
6
�183�
isosceles
72° and 108°
30 cm by 18 cm
38
(x � 1)2 �
(y � 2)2 � 16
936 cm2
6; All faces are squares.
315 cm2
1357.2 m3
168 in3
© Glencoe/McGraw-Hill A26 Glencoe Geometry
Chapter 13 Assessment Answer KeyStandardized Test Practice
Page 771 Page 772
1.
2.
3.
4.
5.
6.
7.
8. E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
E F G H
A B C D9. 10.
11.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
12.
13.
14.
15.
16.
10.25
126 m2
175.9 in2
1526.8 ft3
(0.5, 5.5, �6)
4 2 5
3
© Glencoe/McGraw-Hill A27 Glencoe Geometry
Chapter 13 Assessment Answer KeyUnit 4 Test/Review (Ch. 11–13)
Page 773 Page 774
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
parallelogram;70 units2
9.5 cm
324� � 486�3�in2
33 units2
0.44
triangular prism;bases: �ABC
and �DEF
1009.4 units2
2
129.8 in2
8.5 m
11.
12.
13.
14.
15.
16.
17.
18.
127.5 ft2
181.2 in2
2035.8 cm2
102.4 ft3
1900.7 in3
cylinder
similar
y
x
z
(0, 0, 0)
(0, 0, �3)
(�1, �4, 0)(�1, 0, 0)
(�1, 0, �3)
M(�1, �4, �3)
(0, �4, 0)
(0, �4, �3)
© Glencoe/McGraw-Hill A28 Glencoe Geometry
Chapter 13 Assessment Answer KeySecond Semester Test (Ch. 8–13)
Page 775 Page 776
1.
2.
3.
4.
5.
6.
7.
8.
A
D
B
B
C
A
B
C
9.
10.
11.
12.
13.
14.
15.
16.
17.
A
C
C
A
C
A
D
B
D
© Glencoe/McGraw-Hill A29 Glencoe Geometry
Chapter 13 Assessment Answer KeySecond Semester Test (Ch. 8–13)
Page 777 Page 778
An
swer
s
18.
19.
20.
21.
22.
23.
24.
25.
26.
1800; 30
x � 12; y � 4
Rhombus,rectangle, square;consecutive sides
are ⊥; all sides are �.
(b � c, 0)
25.5
resultant speed:
� 20.4 mph;direction: � 11.3°west of due south
m�1 � 68, m�2 �112, m�3 � 68,
m�4 � 90
34
D�
E�F�
G�
D
EF
G
x
y
O
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
25.5
12.5
30
49.7 mm2
about 0.41
1080 units2
104 cm
sphere
barrel
120 cm3
�453�
© Glencoe/McGraw-Hill A30 Glencoe Geometry
Chapter 13 Assessment Answer KeyFinal Test
Page 779 Page 780
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
D
A
B
D
C
B
A
C
D
A
11.
12.
13.
14.
15.
16.
17.
18.
D
A
A
D
B
B
C
B
© Glencoe/McGraw-Hill A31 Glencoe Geometry
Chapter 13 Assessment Answer KeyFinal Test
Page 781 Page 782
An
swer
s
19.
20.
21.
22.
23.
24.
25.
26.
A
D
C
C
B
A
C
B
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
H
22; 98
hypothesis: a circle
has a radius of r ;conclusion: its
circumference is 2�r
always
60
22; 18
A�G� � E�H�, C�A� � C�E�,�CGH � �CHG
Given
If 2 � of a � are �,then the sidesopposite those
�s are �.
�AGC � �EHC
SSS
centroid
x
y
O
K(3, 4)
© Glencoe/McGraw-Hill A32 Glencoe Geometry
Chapter 13 Assessment Answer KeyFinal Test
Page 783 Page 784
40.
41.
42.
43.
44.
45.
46.
47.
48.
y � 3
5; 35
7
12; 9; 25
52�2� or �73.5;52
m�E � 52, m�F �
127, m�G � 99,m�H � 82
13; 11
5; yes
1 → 2: (x, y) →(x � 3, y � 7);2 → 3: (x, y) →(x � 4, y � 4)
49.
50.
51.
52.
53.
54.
55.
56.
14
112; 68
1387.7 ft2
400�; �0.42
554.1 cm2
hemisphere
�115�;(0.5, �0.5, �10.5)