5-7 Scale Drawings and Scale Models

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5-7 Scale Drawings and Scale Models

Warm UpEvaluate the following for x = 16.

1. 3x 2. x

Evaluate the following for x = .

3. 10x 4. x

48 12

4

34

25

14

110

5-7 Scale Drawings and Scale Models

MG1.2 Construct and read drawings and models made to scale.

California Standards

5-7 Scale Drawings and Scale Models

Vocabulary

scale drawing

scale model

scale

scale factor

5-7 Scale Drawings and Scale Models

A scale drawing is a two-dimensional drawing of an object that is proportional to the object.

A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units.

A scale model is a three-dimensional model that is proportional to the object.

5-7 Scale Drawings and Scale Models

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

Additional Example 1: Finding Actual Measurements

Write a proportion using the scale. Let x be the actual length of the amoeba.

1000 x = 1 8 The cross products are equal.

x = 0.008

The actual length of the amoeba is 0.008 mm.

1000 1 = 8 mm

x mm

Solve the proportion.

5-7 Scale Drawings and Scale Models

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

Check It Out! Example 1

Write a proportion using the scale. Let x be the actual length of the fiber.

10,000 x = 1 1 The cross products are equal.

x = 0.0001

The actual length of the fiber is 0.0001 mm.

10,000 1 = 1 mm

x mm

Solve the proportion.

5-7 Scale Drawings and Scale Models

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 2: Using Proportions to Find Unknown Scales

1 cmx m = 2 cm

8 m

1 8 = x 2 Find the cross products.

8 = 2x

Divide both sides by 2.

The scale is 1 cm:4 m.

4 = x

Set up proportion using scale length .actual length

5-7 Scale Drawings and Scale Models

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

5-7 Scale Drawings and Scale Models

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?

Check It Out! Example 2

1 cmx m = 4 cm

12 m Set up proportion using scale length .actual length

1 12 = x 4 Find the cross products.

12 = 4x

Divide both sides by 4.

The scale is 1 cm:3 m.

3 = x

5-7 Scale Drawings and Scale Models

The ratio of a length on a scale drawing or model to the corresponding length on the actual object is called the scale factor.

When finding a scale factor, you must use the same measurement units. You can use a scale factor to find unknown dimensions.

5-7 Scale Drawings and Scale Models

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?

Additional Example 3: Using Scale Factors to Find Unknown Dimensions

Find the scale factor.

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

118

2 in.3 ft

= 2 in.36 in.

= 1 in.18 in.

= 118

324 = 18h

Convert: 27 ft = 324 in.

Find the cross products.

18 = hThe height of the model is 18 in.

Divide both sides by 18.

118

= h in.324 in.

5-7 Scale Drawings and Scale Models

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?

Check It Out! Example 3

Find the scale factor.

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

16

4 in.2 ft

= 4 in.24 in.

= 1 in.6 in.

= 16

288 = 6h

Convert: 24 ft = 288 in.

Find the cross products.

48 = h

The height of the model is 48 in.Divide both sides by 6.

16

= h in.288 in.

5-7 Scale Drawings and Scale Models

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?

Additional Example 4: Life Science Application

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

5 cm 0.0000001 mm

50 mm 0.0000001 mm= = 500,000,000

Find the scale factor.

5-7 Scale Drawings and Scale ModelsAdditional Example 4 Continued

500,000,000 1

20 cm x cm= Set up a proportion.

500,000,000x = 1(20)

x = 0.00000004

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

Find the cross products.

Divide both sides by 500,000,000.

5-7 Scale Drawings and Scale Models

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?

Check It Out! Example 4

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

2 cm 0.01 mm

20 mm 0.01 mm= = 2,000

Find the scale factor.

5-7 Scale Drawings and Scale ModelsCheck It Out! Example 4 Continued

2,000 1

30 cm x cm= Set up a proportion.

2,000x = 1(30)

x = 0.015

The length of the actual object is 1.5 10-2 cm.

Find the cross products.

Divide both sides by 2,000.

5-7 Scale Drawings and Scale Models

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

drawing of a 22 ft car be?

2. What is the scale of a drawing in which a 9 ft

wall is 6 cm long?

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