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7-8. Scale Models. Course 3. Warm Up. Problem of the Day. Lesson Presentation. 7-8. Scale Models. Course 3. Warm Up The scale of a drawing is 4 in. = 12 ft. Find each actual measurement. 1. 6 in. 2. 2.5 in. The scale of a map is 1 in. = 3.5 mi. Find each length on the map.

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7-8

Scale Models

Course 3

Warm Up

Problem of the Day

Lesson Presentation

7-8

Scale Models

Course 3

Warm Up

The scale of a drawing is 4 in. = 12 ft. Find each actual measurement.

1.6 in. 2. 2.5 in.

The scale of a map is 1 in. = 3.5 mi. Find each length on the map.

3. 21 mi 4. 1.75 mi

18 ft

7.5 ft

6 in.

0.5 in.

7-8

Scale Models

Course 3

Problem of the Day

There is a 2.5-mile racetrack at the Indianapolis Motor Speedway. If a drawing of the racetrack has a scale of 1:1760, what is the length of the track on the drawing?

7.5 ft

7-8

Scale Models

Course 3

Learn to make comparisons between and find dimensions of scale models and actual objects.

7-8

Scale Models

Course 3

Insert Lesson Title Here

Vocabulary

scale model

7-8

Scale Models

Course 3

Very large and very small objects are often modeled. A scale model is a three-dimensional model that accurately represents a solid object. The scale model is mathematically similar to the solid object.

A scale gives the ratio of the dimensions of the model to the actual dimensions.

7-8

Scale Models

1 in.

1

1 in.

1

1 yd

36

36

36 in.

The scale reduces the size of the actual object by a factor of .

Course 3

Additional Example 1A: Analyzing and Classifying Scale Factors

Tell whether each scale reduces, enlarges, or preserves the size of the actual object.

A. 1 in:1 yd

=

=

Convert: 1 yd = 36 in. Simplify.

7-8

Scale Models

100 cm

1 m

10 cm

10 cm

Course 3

Additional Example 1B: Analyzing and Classifying Scale Factors

Tell whether each scale reduces, enlarges, or preserves the size of the actual object.

B. 1 m:10 cm

Convert: 1 m = 100 cm. Simplify.

=

= 10

The scale enlarges the size of the actual object 10 times.

7-8

Scale Models

1 in.

1

1 in.

1

1 ft

12

12

12 in.

The scale reduces the size of the actual object by a factor of .

Course 3

Try This: Example 1A

Tell whether each scale reduces, enlarges, or preserves the size of the actual object.

A. 1 in:1 ft

Convert: 1 ft = 12 in. Simplify.

=

=

7-8

Scale Models

12 in.

1 ft

1 ft

1 ft

Course 3

Try This: Example 1B

Tell whether each scale reduces, enlarges, or preserves the size of the actual object.

B. 12 in:1 ft

=

= 1

Convert: 12 in. = 1 ft. Simplify.

The scale preserves the size of the actual object.

7-8

Scale Models

12 in.

12 in

6 ft

72 in.

The scale factor is , or 1:6.

1

1

6

6

Course 3

Additional Example 2: Finding Scale Factors

What scale factor relates a 12 in. scale model to a 6 ft. man?

12 in:6 ft State the scale.

Write the scale factor as a ratio and simplify.

=

=

7-8

Scale Models

12 in.

12 in

4 ft

48 in.

The scale factor is , or 1:4.

1

1

4

4

Course 3

Try This: Example 2

What scale factor relates a 12 in. scale model to a 4 ft. tree?

12 in:4 ft State the scale.

Write the scale factor as a ratio and simplify.

=

=

7-8

Scale Models

=

=

1 in.

3 in.

3 in.

1

1

The scale factor for the model is . Now set up a proportion.

2 ft

8

24 in.

8

8 in.

h in.

=

384 in.

1

8

Course 3

Additional Example 3: Finding Unknown Dimensions Given Scale Factors

A model of 32 ft tall house was made using the scale 3 in:2 ft. What is the height of the model?

=

First find the scale factor.

Convert: 32 ft = 384 in.

384 = 8h

Cross multiply.

48 = h

Solve for the height.

The height of the model is 48 in.

7-8

Scale Models

=

=

1 in.

4 in.

4 in.

1

1

The scale factor for the model is . Now set up a proportion.

2 ft

6

24 in.

6

6 in.

h in.

=

288 in.

1

6

Course 3

Try This: Example 3

A model of a 24 ft tall bridge was made using the scale 4 in:2 ft. What is the height of the model?

=

First find the scale factor.

Convert: 24 ft = 288 in.

288 = 6h

Cross multiply.

48 = h

Solve for the height.

The height of the model is 48 in.

7-8

Scale Models

=

= 500,000,000

5 cm

50 mm

0.0000001 mm

0.0000001 mm

Course 3

Additional Example 4: Life Science Application

A DNA model was built using the scale 5 cm: 0.0000001 mm. If the model of the DNA chain is 20 cm long, what is the length of the actual chain? Find the scale factor.

The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain.

7-8

Scale Models

500,000,000

20 cm

1

x cm

Course 3

=

Set up a proportion.

500,000,000x = 1(20)

Cross multiply.

x = 0.00000004

Solve for the length.

The length of the DNA chain is 4  10-8 cm.

7-8

Scale Models

=

= 2,000

2 cm

20 mm

0.01 mm

0.01 mm

Course 3

Try This: Example 4

A model was built using the scale 2 cm:0.01 mm. If the model is 30 cm long, what is the length of the actual object? Find the scale factor.

The scale factor for the model is 2,000. This means the actual object is 2 thousand times larger than the model.

7-8

Scale Models

2,000

30 cm

1

x cm

Course 3

Try This: Example 4 Continued

=

Set up a proportion.

2,000x = 1(30)

Cross multiply.

Solve for the length.

x = 0.015

The length of the actual object is 0.015 cm.

7-8

Scale Models

Course 3

Insert Lesson Title Here

Lesson Quiz: Part 1

Tell whether each scale reduces, enlarges, or preserves the size of the actual object.

1. 75 ft:40 in

2. 1 mi:1760 yd

3. 400 m:1 km

4. What scale factor was used to build a 5 in. model of a 60 ft statue?

enlarges

preserves

reduces

1:144

7-8

Scale Models

Course 3

Insert Lesson Title Here

Lesson Quiz: Part 2

5. To create a model of the Eustachian tube of the human ear, an audiologist used the scale 1.5 cm = 0.6 mm. If the diameter of the Eustachian tube is 1.8 mm, what is the diameter of the model?

4.5 cm