Scale Drawing and Scale Models 5-8 Scale Drawing and Scale Models Course 3 Warm Up Problem of the Day Lesson Presentation

Evaluate the following for x = 16. 1. 3x 2. x Warm Up Evaluate the following for x = 16. 1. 3x 2. x Evaluate the following for x = . 3. 10x 4. x 3 4 48 12 2 5 1 4 1 10 4

Problem of the Day An isosceles triangle with a base length of 6 cm and side lengths of 5 cm is dilated by a scale factor of 3. What is the area of the image? 108 cm2

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

Vocabulary scale drawing scale scale model reduction enlargement

A scale drawing is a two-dimensional drawing that accurately represents an object. The scale drawing is mathematically similar 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.

1 unit on the drawing is 20 units. 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

Additional Example 1: Using Proportions to Find Unknown Scales or Lengths 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? 1 cm x m 2 cm 8 m Set up proportion using scale length . actual length = 1  8 = x  2 Find the cross products. 8 = 2x 4 = x Solve the proportion. The scale is 1 cm:4 m.

The scale a:b is read “a to b 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

Check It Out: Example 1 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 cm x m 4 cm 12 m Set up proportion using scale length . actual length = 1  12 = x  4 Find the cross products. 12 = 4x 3 = x Solve the proportion. The scale is 1 cm:3 m.

Additional Example 2: Life Sciences Application Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? 1000 1 = 8 mm x mm scale length actual length 1000  x = 1  8 Find the cross products. x = 0.008 Solve the proportion. The actual length of the amoeba is 0.008 mm.

Check It Out: Example 2 Under a 10,000:1 microscope view, a fiber appears to have length of 1mm. What is its actual length? 10,000 1 = 1 mm x mm scale length actual length 10,000  x = 1  1 Find the cross products. x = 0.0001 Solve the proportion. The actual length of the fiber is 0.0001 mm.

A scale model is a three-dimensional model that accurately represents a solid object. The scale model is mathematically similar to the solid object.

Additional Example 3: Finding Unknown Dimensions Given Scale Factors 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? 2 in. 3 ft = 2 in. 36 in. = 1 in. 18 in. 1 18 = First find the scale factor. The scale factor for the model is . Now set up a proportion. 1 18 1 18 = h in. 324 in. Convert: 27 ft = 324 in. 324 = 18h Cross multiply. 18 = h Solve for the height. The height of the model is 18 in.

Check It Out: Example 3 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? 4 in. 2 ft = 4 in. 24 in. = 1 in. 6 in. 1 6 = First find the scale factor. The scale factor for the model is . Now set up a proportion. 1 6 1 6 = h in. 288 in. Convert: 24 ft = 288 in. 288 = 6h Cross multiply. 48 = h Solve for the height. The height of the model is 48 in.

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. 5 cm 0.0000001 mm 50 mm = = 500,000,000 The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain.

Additional Example 4 Continued 500,000,000 1 20 cm x cm = 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  10-7 cm.

Check It Out: 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. 2 cm 0.01 mm 20 mm = = 2,000 The scale factor for the model is 2,000. This means the actual object is 2 thousand times larger than the model.

Check It Out: Example 4 Continued 2,000 1 30 cm x cm = Set up a proportion. 2,000x = 1(30) Cross multiply. Solve for the length. x = 0.015 The length of the actual object is 1.5 x 10-2 cm.

Lesson Quiz 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? 1 cm = 1.5 ft 1 4 5.5 in. 72 in.