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Course 2

5-9 Scale Drawings and Scale Models

Convert the following measurements.

1. 192 inches = feet

2. 18.5 feet = inches

3. 324 inches = feet

16

222

27

Hmwk: Wbk p 50

EQ: How do I use ratios and proportions in scale drawings?

Course 2

5-9 Scale Drawings and Scale Models

M7G3.b Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures

Vocabulary

scale modelscale factorscalescale drawing

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Course 2

5-9 Scale Drawings and Scale Models

Course 2

5-9 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

5-9 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 shows a 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.

Scale Interpretation

1:20 1 unit on the drawing is 20 units.

1 cm:1 m 1 cm on the drawing is 1 m.

in. = 1 ft in. on the drawing is 1 ft.1 4

1 4

Identify the scale factor.

Additional Example 1: Finding a Scale Factor

Course 2

5-9 Scale Drawings and Scale Models

Room Blueprint

Length (in.) 144 18

Width (in.) 108 13.5

blueprint lengthroom length

= 18

18

The scale factor is .

Write a ratio using one of thedimensions.

18144

=

A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions.

Caution!

A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale?

Additional Example 1: Using Proportions to Find Unknown Scales or Lengths

1 cmx m = 2 cm

8 m

The scale is 1 cm:4 m.

4 = x

Set up proportion using scale length .actual length

The scale a:b is read “a to b.” For example, the scale 1 cm:4 m is read “one centimeter to four meters.”

Reading Math

The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale?

1 cmx m =

4 cm12 m Set up proportion using scale length .

actual length

The scale is 1 cm:3 m.

3 = x

Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length?

scale length actual length

x = 0.008

The actual length of the amoeba is 0.008 mm.

1000 1 = 8 mm

x mm

Under a 10,000:1 microscope view, a fiber appears to have length of 1mm. What is its actual length?

scale length actual length

x = 0.0001

The actual length of the fiber is 0.0001 mm.

10,000 1 = 1 mm

x mm

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Course 2

5-9 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

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.

Course 2

5-9 Scale Drawings and Scale Models

51

posterphoto

= 51

36 l

= 51

l = 7.2

Write a proportion to find the length l.

Course 2

5-9 Scale Drawings and Scale Models

posterphoto = 5

120.5

w= 5

1

w = 4.1

Write a proportion to find the width w.

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

Course 2

5-9 Scale Drawings and Scale ModelsMary’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

dollhouseblueprint

= 1.51

l = 67.5

Write a proportion to find the length l.

Multiply.

l 45

= 1.51

Course 2

5-9 Scale Drawings and Scale Models

w 24

= 1.51

w = 36

Write a proportion to find the width w.

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

dollhouseblueprint

= 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?

Course 2

5-9 Scale Drawings and Scale Models

1.560

= 7.5d

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

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Course 2

5-9 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?

150

= 7d

d = 350

The distance between the cities is 350 kilometers.

A model of a 27 ft tall house was made using a scale of 2 in.:3 ft. What is the height of the model?

18 = h

The height of the model is 18 in.

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

48 = h

The height of the model is 48 in.

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?

x = 0.15mm

Lesson Quiz: Part I

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Course 2

5-9 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 II

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Course 2

5-9 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

1. What is the scale of a drawing in which a 9 ft wall is 6 cm long?

2. Using a in. = 1 ft scale, how long would a

drawing of a 22 ft car be?

3. The height of a person on a scale drawing is

4.5 in. The scale is 1:16. What is the actual height

of the person?

Lesson Quiz

5.5 in.

1 cm = 1.5 ft

72 in.

14