4 10 Scale Drawings and Scale Models Warm

4 -10 Scale Drawings and Scale Models Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

4 -10 Scale Drawings and Scale Models Warm Up Write each fraction in the simplest form. 4 1 1. 48 12 2. 9 135 1 15 Convert the following measurements. 3. 192 inches = 4. 18. 5 feet = 5. 324 inches = feet 16 inches 222 feet 27

4 -10 Scale Drawings and Scale Models I can understand ratios and proportions in scale drawings. I can use ratios and proportions with scale.

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 -dimensional drawing of an object. two Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. For example, if a drawing of a building has 1 a scale factor of , this means that each 3 1 dimension of the drawing is 3 of the corresponding dimension of the actual building.

4 -10 Scale Drawings and Scale Models A scale model is a proportional - dimensional model of an object. three 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 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 Additional Example 3: Measurement Application On a road map, the distance between Pittsburgh and Philadelphia is 7. 5 inches. What is the actual distance between the cities if the map scale is 1. 5 inches = 60 miles? 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 1 Identify the scale factor. Model Aircraft Blueprint Length (in. ) 12 2 Wing span (in. ) 18 3 blueprint length = 2 aircraft length 12 Write a ratio using one of the dimensions. = 1 6 1 The scale factor is 6. Simplify.

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 1. 5 factor is 1. Find the size of the dollhouse. Think: dollhouse = 1. 5 blueprint 1 l = 1. 5 45 1 Write a proportion to find the length l. l = 45 · 1. 5 Find the cross products. l = 67. 5 Multiply.

4 -10 Scale Drawings and Scale Models Check It Out: Example 2 Continued 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 1. 5 factor is 1. Find the size of the dollhouse. Think: dollhouse = 1. 5 blueprint 1 w = 1. 5 24 1 Write a proportion to find the width w. w = 24 · 1. 5 Find the cross products. Multiply. w = 36 The dollhouse is 67. 5 inches long and 36 inches wide.

4 -10 Scale Drawings and Scale Models Check It Out: Example 3 On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers? Let d be the actual distance between the cities. 1=7 Write a proportion. 50 d 1 · d = 50 · 7 1 d = 350 Find the cross products. Multiply. d = 350 The distance between the cities is 350 kilometers.

4 -10 Scale Drawings and Scale Models Lesson Quizzes Standard Lesson Quiz for Student Response Systems

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. What is the actual distance between the cities if the map scale is 3 cm = 90 km? 330 km

4 -10 Scale Drawings and Scale Models Lesson Quiz for Student Response Systems 1. Identify the scale factor. Length (cm) A. C. 110 20 B. D. 120 10 Fish Model 120 12

4 -10 Scale Drawings and Scale Models Lesson Quiz for Student Response Systems 2. On a scale drawing, the height of a building 1 is 60 inches. The scale factor is. What is 15 the height of the actual building? A. 240 in. , or 20 ft B. 300 in. , or 25 ft C. 600 in. , or 50 ft D. 900 in. , or 75 ft

4 -10 Scale Drawings and Scale Models Lesson Quiz for Student Response Systems 3. On a road map, the distance from Washington, DC to New York is 15 cm. What is the actual distance between the cities if the map scale is 3 cm = 50 mi? A. 150 mi B. 200 mi C. 250 mi D. 300 mi