Pre-Algebra 7-9 Scaling Three-Dimensional Figures 7-9 Scaling Three-Dimensional Figures Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day.

Pre-Algebra

7-9 Scaling Three-Dimensional Figures7-9 Scaling Three-Dimensional Figures

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

7-9 Scaling Three-Dimensional Figures

Warm UpFind the surface area of each rectangular prism.

1. length 14 cm, width 7 cm, height 7 cm

2. length 30 in., width 6 in., height 21 in

3. length 3 mm, width 6 mm, height 4 mm

4. length 37 in., width 9 in., height 18 in.

490 cm2

1872 in2

108 mm2

Pre-Algebra


2322 in2

Pre-Algebra


Problem of the Day

A model of a solid-steel machine tool is built to a scale of 1 cm = 10 cm. The real object will weigh 2500 grams. How much does the model, also made of solid steel, weigh? 2.5 g

Pre-Algebra


Learn to make scale models of solid figures.

Pre-Algebra


Vocabulary

capacity

Pre-Algebra


Pre-Algebra


Corresponding edge lengths of any two cubes are in proportion to each other because the cubes are similar. However, volumes and surface areas do not have the same scale factor as edge lengths.

Each edge of the 2 ft cube is 2 times as long as each edge of the 1 ft cube. However, the cube’s volume, or capacity, is 8 times as large, and its surface area is 4 times as large as the 1 ft cube’s.

Pre-Algebra


Multiplying the linear dimensions of a solid by n creates n2 as much surface area and n3 as much volume.

Helpful Hint

Pre-Algebra


A 3 cm cube is built from small cubes, each 1 cm on an edge. Compare the following values.

A. the edge lengths of the large and small cubes

Additional Example 1A: Scaling Models That Are Cubes

3 cm cube1 cm cube

3 cm1 cm

Ratio of corresponding edges

The edges of the large cube are 3 times as long as the edges of the small cube.

= 3

Pre-Algebra


B. the surface areas of the two cubes

Additional Example 1B: Scaling Models That Are Cubes

3 cm cube1 cm cube

54 cm2

6 cm2

Ratio of corresponding areas

The surface area of the large cube is 9 times that of the small cube.

= 9

Pre-Algebra


C. the volumes of the two cubes

Additional Example 1C: Scaling Models That Are Cubes

3 cm cube1 cm cube

27 cm3

1 cm3

Ratio of corresponding volumes

The volume of the large cube is 27 times that of the small cube.

= 27

Pre-Algebra



A. the edge lengths of the large and small cubes

Try This: Example 1A

2 cm cube1 cm cube

2 cm1 cm

Ratio of corresponding edges

The edges of the large cube are 2 times as long as the edges of the small cube.

= 2

Pre-Algebra


B. the surface areas of the two cubes

Try This: Example 1B

2 cm cube1 cm cube

24 cm2

6 cm2

Ratio of corresponding areas

The surface area of the large cube is 4 times that of the small cube.

= 4

Pre-Algebra


C. the volumes of the two cubes

Try This: Example 1C

2 cm cube1 cm cube

8 cm3

1 cm3

Ratio of corresponding volumes

The volume of the large cube is 8 times that of the small cube.

= 8

Pre-Algebra


A box is in the shape of a rectangular prism. The box is 4 ft tall, and its base has a length of 3 ft and a width of 2 ft. For a 6 in. tall model of the box, find the following.

A. What is the scale factor of the model?

Additional Example 2: Scaling Models That Are Other Solid Figures

The scale factor of the model is 1:8.

Convert and simplify.18

6 in.4 ft

= 6 in.48 in.

=

Pre-Algebra


B. What are the length and the width of the model?

Additional Example 2B: Scaling Models That Are Other Solid Figures

Length: 3 ft = in. = 4 in.18

36 8

12

Width: 2 ft = in. = 3 in.18

24 8

The length of the model is 4 in., and the width is 3 in.

12

Pre-Algebra


A box is in the shape of a rectangular prism. The box is 8 ft tall, and its base has a length of 6 ft and a width of 4 ft. For a 6 in. tall model of the box, find the following.

A. What is the scale factor of the model?

Try This: Example 2A

The scale factor of the model is 1:16.

Convert and simplify.6 in.8 ft

= 6 in.96 in.

= 116

Pre-Algebra


B. What are the length and the width of the model?

Try This: Example 2B

Length: 6 ft = in. = 4 in. 116

7216

12

Width: 4 ft = in. = 3 in. 116

4816

The length of the model is 4 in., and the width is 3 in.

12

Pre-Algebra


It takes 30 seconds for a pump to fill a cubic container whose edge measures 1 ft. How long does it take for the pump to fill a cubic container whose edge measures 2 ft?

Additional Example 3: Business Application

V = 2 ft 2 ft 2 ft = 8 ft3 Find the volume of the 2 ft cubic container.

Set up a proportion and solve.

Cancel units.

30 8 = x

240 = xIt takes 240 seconds, or 4 minutes, to fill the larger container.

Multiply.

Calculate the fill time.

30 s1 ft3

x 8 ft3

=

Pre-Algebra


It takes 30 seconds for a pump to fill a cubic container whose edge measures 1 ft. How long does it take for the pump to fill a cubic container whose edge measures 3 ft?

Try This: Example 3

Set up a proportion and solve.

V = 3 ft 3 ft 3 ft = 27 ft3 Find the volume of the 2 ft cubic container.

30 27 = x

810 = xIt takes 810 seconds, or 13.5 minutes, to fill the larger container.

Multiply.

Calculate the fill time.

30 s1 ft3

x 27 ft3

=

Pre-Algebra



1. the edge lengths of the two cubes

2. the surface areas of the two cubes

3. the volumes of the two cubes

Lesson Quiz: Part 1

Pre-Algebra


4. A pyramid has a square base measuring 185 m on each side and a height of 115 m. A model of it has a base 37 cm on each side. What is the height of the model?

5. A cement truck is pouring cement for a new 4 in. thick driveway. The driveway is 90 ft long and 20 ft wide. How long will it take the truck to pour the cement if it releases 10 ft3 of cement per minute?

Lesson Quiz: Part 2

Pre-Algebra 7-9 Scaling Three-Dimensional Figures 7-9 Scaling Three-Dimensional Figures Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day.

Documents

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scaling models

solid figures length

ft cubes

scale models of solid

small cubes additional

g slide

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