Measurement in Three-Dimensional Figures9-10

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Measurement in Three-Dimensional Figures9-10

Warm UpFill in the blanks.

1. 1 yd = ___ in.

2. 1 mi ___ ft

3. 1 mi ___ km

4. Find the surface are and volume of a cube with a

side length of 3 meters.

36

3.28

1.6

54 m2, 27 m3

Measurement in Three-Dimensional Figures9-10

Problem of the Day

Chris cuts 1 in. by 1 in. squares from the corners of an 8.5 in. by 11 in. paper and fold the sides up to form an open box. What is the volume of a box?

58.5 in2

Measurement in Three-Dimensional Figures9-10

MA.8.G.5.1 Compare, contrast, and convert units of measure between different measurement systems (U.S. customary or metric (SI)) and dimensions including…area, volume, and derived units to solve problems.

Sunshine State Standards

Measurement in Three-Dimensional Figures9-10

You can convert units of area and volume. For example, you can draw a diagram to help you convert square feet to square inches.

You can convert units of area by squaring the linear conversion factor.

Measurement in Three-Dimensional Figures9-10

A shoebox has a length of 13 inches, a width of 9 inches, and a height of 4 1/2 inches. Find the surface area of the box in square centimeters.

Additional Example 1: Converting Units of Measure

Multiply each area by 2.

Step 1: Find the area in square inches.

A = lw

A = 13 9A = 117 in2

A = lw

A = 9 4.5

A = 40.5 in2

A = lw

A = 13 4.5

A = 58.5 in2

A = 2(117 + 40.5 + 58.5) in2

A = 432 in2

Measurement in Three-Dimensional Figures9-10

Step 2: Find the conversion factor for inches to centimeters.

1 inch 2.54 cm

A shoebox has a length of 13 inches, a width of 9 inches, and a height of 4 1/2 inches. Find the surface area of the box in square centimeters.

Additional Example 1 Continued

Measurement in Three-Dimensional Figures9-10

Square the linear conversion factor.

A shoebox has a length of 13 inches, a width of 9 inches, and a height of 4 1/2 inches. Find the surface area of the box in square centimeters.

Additional Example 1 Continued

Step 3: Convert the area.

The surface area of the box in square centimeters is 2787.1 cm2.

Measurement in Three-Dimensional Figures9-10

Check It Out: Example 1A cone has a radius of 3 centimeters, a height of 4 centimeters, and a slant height of 5 centimeters. What is the surface area of the cone in square inches to the nearest tenth? Use 3.14 for π.

S = 3.14(3)2 + 3.14(3)(5) = 28.26 + 47.1 = 75.36 cm2

75.36 cm2 = 11.68082336 in21 in2.54 cm

2

The surface area of the cone is about 11.7 in2.

Measurement in Three-Dimensional Figures9-10

A standard beverage can is a cylinder with a radius of 3.25 cm and a height of 10.7 cm. What is the volume of the can in cubic inches to the nearest tenth?

Additional Example 2: Converting Units of Volume

Step 1: Find the volume in cubic centimeters.

V = r2h

(3.14)(3.25)2(10.7)

354.9 cm3

Measurement in Three-Dimensional Figures9-10

A standard beverage can is a cylinder with a radius of 3.25 cm and a height of 10.7 cm. What is the volume of the can in cubic inches to the nearest tenth?

Additional Example 2 Continued

Step 2: Convert the volume.

The volume of the can in cubic inches is about 21.7 in3.

Measurement in Three-Dimensional Figures9-10

Find the approximate volume of the cone in cubic feet.

Check It Out: Example 2

V = r2h

The volume of the cone is about 73.9 ft3.

13

= (3.14) (1)2 (2)13

= 2.093 m3_

2.093 m3 = 73.925369 ft3_ 1 ft

0.3048m2

Measurement in Three-Dimensional Figures9-10

An archaeologist wants to apply a liquid solution to the lateral area of a square pyramid as a protectant. Each side of the square base measures 12 meters and the slant height is 10 meters. One gallon of solution covers 200 ft2. About how many gallons of a solution does the archaeologist need to cover the lateral area of the pyramid?

Additional Example 3: Application

Step 1: Find the lateral surface area of the pyramid.

Measurement in Three-Dimensional Figures9-10

Additional Example 3 Continued

Step 2: Convert square meters to square feet.

1 m2 10.8 ft2, so 240 m2 2592 ft2.

Step 3: Find how many gallons of solution will cover 2592 ft2.

= 12.96 gal

It will take about 13 gallons to cover the lateral area of the pyramid.

Measurement in Three-Dimensional Figures9-10

The concrete tile shown is a hexagonal prism. A cubic yard of concrete weighs about 3600 pounds. What is the weight of 40 tiles in tons.

Check It Out: Example 3

Measurement in Three-Dimensional Figures9-10

Check It Out: Example 3 Continued

Volume of 1 tile in cubic feet:

6 • (3)(2.6)(1) = 23.4 ft312

Volume in cubic yards:

23.4 ft3 = 0.87 yd31 yd3 ft

3

0.87 yd3 • = 3132 lb3600 lb1 yd3

1 tile: 3132 lb = 1.57 tons1 ton2000 lb

40 tiles: 40 • 1.57 tons = 62.8 tons

Measurement in Three-Dimensional Figures9-10

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Measurement in Three-Dimensional Figures9-10

1. A triangle has a base of 8 inches and a height of 22 inches. Find the area of the triangle in square centimeters.

2. Find the volume of the pyramid in cubic yards.

3. A child is coloring a circle with a radius of 9

centimeters at a rate of 0.5 square inch per second.

How long will it take the child to color the circle? Use

3.14 for .

Lesson Quiz

671.41 yd3

567.74 cm2

78.9 s

Measurement in Three-Dimensional Figures9-10

1. Convert. 1 mi3 = ___ yd3

A. 1760

B. 3,097,600

C. 5,451,776,000

D. 3

Lesson Quiz for Student Response Systems

Measurement in Three-Dimensional Figures9-10

2. Find the volume.

A. 52 in3

B. 52 in2

C. 7800 in3

D. 7800 in2

Lesson Quiz for Student Response Systems

Measurement in Three-Dimensional Figures9-10

3. Find the volume.

A. 7800 ft3

B. 650 ft3

C. 4.5 ft3

D. 54.2 ft3

Lesson Quiz for Student Response Systems