5 8 Scale Drawings Drawing and Scale Models

5 -8 Scale. Drawings Drawing and Scale Models Warm Up Problem of the Day Lesson Presentation Course 33

5 -8 Scale Drawings and Scale Models Warm Up Evaluate the following for x = 16. 1. 3 x 48 2. 3 x 4 12 Evaluate the following for x = 2. 5 1 1 x 3. 10 x 4. 4 10 4 Course 3

5 -8 Scale Drawings and Scale Models 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 cm 2 Course 3

5 -8 Scale Drawings and Scale Models Learn to make comparisons between and find dimensions of scale drawings, models, and actual objects. Course 3

5 -8 Scale Drawings and Scale Models Vocabulary scale drawing scale model reduction enlargement Course 3

5 -8 Scale Drawings and Scale Models 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. Course 3

5 -8 Scale Drawings and Scale Models Scale Interpretation 1: 20 1 unit on the drawing is 20 units. 1 cm: 1 m 1 cm on the drawing is 1 m. 1 4 in. = 1 ft Course 3 1 in. on the drawing is 1 ft. 4

5 -8 Scale Drawings and Scale Models 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 xm = 1 8= 8= 2 cm scale length. Set up proportion using 8 m actual length x 2 Find the cross products. 2 x 4=x Solve the proportion. The scale is 1 cm: 4 m. Course 3

5 -8 Scale Drawings and Scale Models Reading Math The scale a: b is read “a to b. ” For example, the scale 1 cm: 4 m is read “one centimeter to four meters. ” Course 3

5 -8 Scale Drawings and Scale Models 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 4 cm scale length. = Set up proportion using xm 12 m actual length 1 12 = x 4 Find the cross products. 12 = 4 x 3=x Solve the proportion. The scale is 1 cm: 3 m. Course 3

5 -8 Scale Drawings and Scale Models 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 = 8 mm 1 x mm 1000 x=1 8 x = 0. 008 scale length actual length Find the cross products. Solve the proportion. The actual length of the amoeba is 0. 008 mm. Course 3

5 -8 Scale Drawings and Scale Models Check It Out: Example 2 Under a 10, 000: 1 microscope view, a fiber appears to have length of 1 mm. What is its actual length? 10, 000 = 1 mm 1 x mm 10, 000 x=1 1 x = 0. 0001 scale length actual length Find the cross products. Solve the proportion. The actual length of the fiber is 0. 0001 mm. Course 3

5 -8 Scale Drawings and Scale Models A scale model is a three-dimensional model that accurately represents a solid object. The scale model is mathematically similar to the solid object. Course 3

5 -8 Scale Drawings and Scale Models 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. = 1 First find the scale factor. 3 ft 36 in. 18 1. Now set up a The scale factor for the model is 18 proportion. 1 = h in. Convert: 27 ft = 324 in. 18 324 in. 324 = 18 h Cross multiply. 18 = h Solve for the height. The height of the model is 18 in. Course 3

5 -8 Scale Drawings and Scale Models 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. = 1 in. 1 = First find the scale factor. 2 ft 24 in. 6 The scale factor for the model is 1 6. Now set up a proportion. 1 = h in. Convert: 24 ft = 288 in. 6 288 in. 288 = 6 h 48 = h Cross multiply. Solve for the height. The height of the model is 48 in. Course 3

5 -8 Scale Drawings and Scale Models 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 50 mm = 0. 0000001 mm = 500, 000 The scale factor for the model is 500, 000. This means the model is 500 million times larger than the actual chain. Course 3

5 -8 Scale Drawings and Scale Models Additional Example 4 Continued 500, 000 = 20 cm 1 x cm 500, 000 x = 1(20) x = 0. 00000004 Set up a proportion. Cross multiply. Solve for the length. The length of the DNA chain is 4 10 -7 cm. Course 3

5 -8 Scale Drawings and Scale Models 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 20 mm = 2, 000 = 0. 01 mm The scale factor for the model is 2, 000. This means the actual object is 2 thousand times larger than the model. Course 3

5 -8 Scale Drawings and Scale Models Check It Out: Example 4 Continued 2, 000 = 30 cm 1 x cm Set up a proportion. 2, 000 x = 1(30) Cross multiply. x = 0. 015 Solve for the length. The length of the actual object is 1. 5 x 10 -2 cm. Course 3

5 -8 Scale Drawings and Scale Models Lesson Quiz 1. What is the scale of a drawing in which a 9 ft wall is 6 cm long? 1 cm = 1. 5 ft 2. Using a 1 in. = 1 ft scale, how long would a 4 drawing of a 22 ft car be? 5. 5 in. 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? 72 in. Course 3