5-7 Scale Drawings and Scale Models

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpWrite each fraction in the simplest form.

Course 2

5-7 Scale Drawings and Scale Models

1. 4

482. 9

135

Convert the following measurements.

3. 192 inches = feet

4. 18.5 feet = inches

5. 324 inches = feet

16

222

27

112

115

Problem of the Day

A toy model of a 200 foot dinosaur is 3 in. long. How many times as long as the model is the dinosaur? 800 times as long

Course 2

5-7 Scale Drawings and Scale Models

Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.

Course 2

5-7 Scale Drawings and Scale Models

Vocabulary

scale modelscale factorscalescale drawing

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Course 2

5-7 Scale Drawings and Scale Models

Course 2

5-7 Scale Models and Scale Drawings

This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO

gauge model train is . 1

87

This means that each dimension of the model is of the corresponding dimension of the actual train.

187

Course 2

5-7 Scale Models and Scale Drawings

A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph showsa scale drawing of the model train.

A scale drawing is a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

Identify the scale factor.

Additional Example 1: Finding a Scale Factor

Course 2

5-7 Scale Drawings and Scale Models

Room Blueprint

Length (in.) 144 18

Width (in.) 108 13.5

blueprint lengthroom length

= 1818

The scale factor is .

Write a ratio using one of thedimensions.

Simplify.

18144

=

Try This: Example 1

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Course 2

5-7 Scale Drawings and Scale Models

Identify the scale factor.

Model Aircraft Blueprint

Length (in.) 12 2

Wing span (in.) 18 3

blueprint length aircraft length

= 212

= 16

The scale factor is .16

Write a ratio using one of the dimensions.

Simplify.

A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale

factor is . Find the size of the photograph.

Additional Example 2: Using Scale Factors to Find Unknown Lengths

Course 2

5-7 Scale Drawings and Scale Models

51

Think: posterphoto

= 51

36 l

= 51

5l = 36

l = 7.2

Write a proportion to find the length l.

Find the cross products.

Divide.

A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale

factor is . Find the size of the photograph.

Additional Example 2 Continued

Course 2

5-7 Scale Drawings and Scale Models

51

Think: posterphoto

= 51

20.5 w

= 51

5w = 20.5

w = 4.1

Write a proportion to find the width w.

Find the cross products.

Divide.The photo is 7.2 in. long and 4.1 in. wide.

Try This: Example 2

Course 2

5-7 Scale Drawings and Scale Models

Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse.

1.51

Think: dollhouseblueprint

= 1.51

l = 45 · 1.5

l = 67.5

Write a proportion to find the length l.

Find the cross products.

Multiply.

l 45

= 1.51

Try This 2 Continued

Course 2

5-7 Scale Drawings and Scale Models

w 24

= 1.51

w = 24 · 1.5

w = 36

Write a proportion to find the width w.

Find the cross products.

Multiply.The dollhouse is 67.5 inches long and 36 inches wide.

Think: dollhouseblueprint

= 1.51

Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse.

1.51

On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles?

Additional Example 3: Measurement Application

Course 2

5-7 Scale Drawings and Scale Models

Let d be the actual distance between the cities.1.560

= 7.5d

1.5 · d = 60 · 7.5

1.5d = 450

1.5d1.5

= 4501.5

d = 300The distance between the cities is 300 miles.

Write a proportion.

Find the cross products.

Multiply.

Divide.

Try This: Example 3

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Course 2

5-7 Scale Drawings and Scale Models

On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers?

Let d be the actual distance between the cities.1

50= 7

d1 · d = 50 · 7

1d = 350

d = 350

The distance between the cities is 350 kilometers.

Write a proportion.

Find the cross products.

Multiply.

Lesson Quiz: Part 1

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Course 2

5-7 Scale Drawings and Scale Models

Identify the scale factor.

Statue of Liberty Model

Height (in.) 1,824 8

1.

2.

144 inches, or 12 feet

1228

On a scale drawing, a kitchen wall is 6 inches long.

The scale factor is . What is the length of the

actual wall?

124

Lesson Quiz: Part 2

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Course 2

5-7 Scale Drawings and Scale Models

3. On a road map, the distance from Green Bay toChicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km?

330 km