4 10 Scale Drawings and Scale Models Vocabulary

4 -10 Scale Drawings and Scale Models Vocabulary scale drawing scale factor scale model scale

4 -10 Scale Drawings and Scale Models A scale drawing is a proportional two-dimensional drawing of an object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor.

4 -10 Scale Drawings and Scale Models A scale model is a proportional threedimensional model of an object. 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.

4 -10 Scale Drawings and Scale Models Additional Example 1: Finding a Scale Factor Identify the scale factor. Length (in. ) Width (in. ) blueprint length = 18 144 room length = 1 8 The scale factor is 1. 8 Room 144 108 Blueprint 18 13. 5 Write a ratio using one of the dimensions. Simplify. Caution! A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions.

4 -10 Scale Drawings and Scale Models Check It Out: Example 1 Identify the scale factor. Model Aircraft Blueprint Length (in. ) 12 2 Wing span (in. ) 18 3 blueprint length = 2 = 1 model length 6 12

4 -10 Scale Drawings and Scale Models Additional Example 2: Using Scale Factors to Find Unknown Lengths A photograph was enlarged and made into a poster. The poster is 20. 5 inches by 36 inches. 5 The scale factor is. Find the size of the 1 photograph. poster = 5 Think: photo 1 36 = 5 l 1 5 l = 36 l = 7. 2 Write a proportion to find the length l. Find the cross products. Divide.

4 -10 Scale Drawings and Scale Models Additional Example 2 Continued A photograph was enlarged and made into a poster. The poster is 20. 5 inches by 36 inches. The scale factor is 5. Find the size of the 1 photograph. Think: poster = 5 photo 1 20. 5 = 5 w 1 5 w = 20. 5 w = 4. 1 Write a proportion to find the width w. Find the cross products. Divide. The photo is 7. 2 in. long and 4. 1 in. wide.

4 -10 Scale Drawings and Scale Models Check It Out: Example 2 Mary’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 1. 5. Find the size of the dollhouse. 1 dollhouse = 1. 5; 1. 5 = x ; x = 1. 5 · 24= 36 1 blueprint 1 1 24 1. 5 = y ; y = 1. 5 · 45 = 67. 5 1 45 1 The dollhouse is 36 in. by 67. 5 in.

4 -10 Scale Drawings and Scale Models Additional Example 3: Measurement Application On a road map with a scale 1. 5 inches: 60 miles, the distance between Pittsburgh and Philadelphia measures 7. 5 inches. What is the actual distance between the two cities? Let d be the actual distance between the cities. 1. 5 = 7. 5 Write a proportion. 60 d 1. 5 · d = 60 · 7. 5 Find the cross products. 1. 5 d = 450 Multiply. 1. 5 d = 450 Divide both sides by 1. 5 d = 300 The distance between the cities is 300 miles.

4 -10 Scale Drawings and Scale Models Check It Out: Example 3 A On a road map with a scale of 1 inch : 50 kilometers, the distance between Dallas and Houston is 7 inches. What is the actual distance between the two cities? 1=7 50 x x = 7 · 50 x = 350 km

4 -10 Scale Drawings and Scale Models Check It Out: Example 3 B On a road map with a scale of 0. 5 inch : 40 miles, the distance between Tallahassee and Orlando is 3 inches. What is the actual distance between the two cities? 0. 5 = 3 40 x 0. 5 x = 120 x = 240 miles

4 -10 Scale Drawings and Scale Models Lesson Quiz: Part I Identify the scale factor. 1. Height (in. ) Statue of Liberty Model 1, 824 8 1 228 2. On a scale drawing, a kitchen wall is 6 inches long. 1 The scale factor is. What is the length of the 24 actual wall? 144 inches, or 12 feet

4 -10 Scale Drawings and Scale Models Lesson Quiz: Part II 3. On a road map, the distance from Green Bay to Chicago is 11 cm. The map scale is 3 cm: 90 km. What is the actual distance between two cities? 330 km