5 -7 Scale Drawings and Scale Models California

5 -7 Scale Drawings and Scale Models California Standards MG 1. 2 Construct and read drawings and models made to scale.

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 model is a three-dimensional model 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.

5 -7 Scale Drawings and Scale Models Additional Example 1: Finding Actual Measurements Under a 1000: 1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? Write a proportion using the 1000 8 mm scale. Let x be the actual = x mm 1 length of the amoeba. 1000 x=1 8 x = 0. 008 The cross products are equal. Solve the proportion. The actual length of the amoeba is 0. 008 mm.

5 -7 Scale Drawings and Scale Models Check It Out! Example 1 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 Write a proportion using the scale. Let x be the actual length of the fiber. The cross products are equal. Solve the proportion. The actual length of the fiber is 0. 0001 mm.

5 -7 Scale Drawings and Scale Models Additional Example 2: Using Proportions to Find Unknown Scales 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 = 2 cm Set up proportion using scale length. xm 8 m actual length 1 8 = x 2 Find the cross products. 8 = 2 x 4=x Divide both sides by 2. The scale is 1 cm: 4 m.

5 -7 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. ”

5 -7 Scale Drawings and Scale Models Check It Out! Example 2 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 = 12 cm Set up proportion using scale length. xm m actual length 1 12 = x 4 12 = 4 x 3=x Find the cross products. Divide both sides by 4. The scale is 1 cm: 3 m.

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 Additional Example 3: Using Scale Factors to Find Unknown Dimensions 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 Find the scale factor. 3 ft 36 in. 18 1 The scale factor for the model is 18. Now set up a proportion. 1 = h in. Convert: 27 ft = 324 in. 18 324 in. 324 = 18 h Find the cross products. 18 = h Divide both sides by 18. The height of the model is 18 in.

5 -7 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 = Find the scale factor. 2 ft 24 in. 6 The scale factor for the model is 1. Now set up a 6 proportion. 1 = h in. Convert: 24 ft = 288 in. 6 288 in. 288 = 6 h 48 = h Find the cross products. Divide both sides by 6. The height of the model is 48 in.

5 -7 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 0. 0000001 mm The scale factor for the model is 500, 000. This means the model is 500 million times larger than the actual chain.

5 -7 Scale Drawings and Scale Models Additional Example 4 Continued 500, 000 = 20 cm 1 x cm 500, 000 x = 1(20) Set up a proportion. Find the cross products. Divide both sides by x = 0. 00000004 500, 000. The length of the DNA chain is 4 10 -8 cm.

5 -7 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 two thousand times larger than the model.

5 -7 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) Find the cross products. x = 0. 015 Divide both sides by 2, 000. The length of the actual object is 1. 5 10 -2 cm.