5-7 Scale Drawings and Scale Models
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1 5-7 Scale Drawings and Scale Models Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.
2 5-7 Scale Insert Drawings Lesson Title and Here Scale Models scale model scale factor scale scale drawing Vocabulary
3 5-7 Scale Models and Scale Drawings This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO gauge model train is 87. This means that each dimension of the model is 87 of the corresponding dimension of the actual train.
4 5-7 Scale Models and Scale Drawings 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. A scale drawing is a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.
5 5-7 Scale Drawings and Scale Models Additional Example : Finding a Scale Factor Identify the scale factor. blueprint length room length Room Blueprint Length (in.) 44 8 Width (in.) = 8 44 = 8 The scale factor is. 8 Write a ratio using one of the dimensions. Simplify.
6 5-7 Insert Scale Drawings Lesson Title and Here Scale Models Try This: Example Identify the scale factor. Model Aircraft Blueprint Length (in.) 2 2 Wing span (in.) 8 3 blueprint length aircraft length = 2 2 = 6 The scale factor is. 6 Write a ratio using one of the dimensions. Simplify.
7 5-7 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. The scale factor is 5 Think: poster photo = 5. Find the size of the photograph. 36 L = 5 5L = 36 Write a proportion to find the length L. Find the cross products. L = 7.2 Divide.
8 5-7 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 Think: poster photo = 5. Find the size of the photograph w = 5 5w = 20.5 Write a proportion to find the width w. Find the cross products. w = 4. Divide. The photo is 7.2 in. long and 4. in. wide.
9 5-7 Scale Drawings and Scale Models Try This: 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.5. Find the size of the dollhouse. Think: dollhouse blueprint =.5 L 45 =.5 L = 45.5 L = 67.5 Write a proportion to find the length L. Find the cross products. Multiply.
10 5-7 Scale Drawings and Scale Models Try This 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 factor is.5. Find the size of the dollhouse. Think: dollhouse blueprint =.5 w 24 =.5 w = 24.5 Write a proportion to find the width w. Find the cross products. w = 36 Multiply. The dollhouse is 67.5 inches long and 36 inches wide.
11 5-7 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.5 inches = 60 miles? Let d be the actual distance between the cities = 7.5 d.5 d = d = 450.5d.5 = d = 300 Write a proportion. Find the cross products. Multiply. Divide. The distance between the cities is 300 miles.
12 5-7 Insert Scale Drawings Lesson Title and Here Scale Models Try This: 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 inch = 50 kilometers? Let d be the actual distance between the cities. 50 = 7 d d = 50 7 d = 350 d = 350 Write a proportion. Find the cross products. Multiply. The distance between the cities is 350 kilometers.
13 5-7 Scale Insert Drawings Lesson Title and Here Scale Models Lesson Quiz: Part Identify the scale factor.. Statue of Liberty Model Height (in.), On a scale drawing, a kitchen wall is 6 inches long. The scale factor is. What is the length of the 24 actual wall? 44 inches, or 2 feet
14 5-7 Scale Insert Drawings Lesson Title and Here Scale Models Lesson Quiz: Part 2 3. On a road map, the distance from Green Bay to Chicago is cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km? 330 km
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