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Course 2

5-9. Scale Models and Scale Drawings.

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Course 2

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  1. 5-9 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 . 1 87 1 87 This means that each dimension of the model is of the corresponding dimension of the actual train. Course 2

  2. 5-9 Scale Models and Scale Drawings Course 2 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 drawingis a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

  3. Scale Factor: The ratio of corresponding lengths of the sides of two similar figures.

  4. 5-9 Scale Drawings and Scale Models 18 144 Caution! A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions. 1 8 The scale factor is . Course 2 Example #1 Identify the scale factor. blueprint length room length Write a ratio using one of the dimensions. = 1 8 = Simplify.

  5. 5-9 Scale Drawings and Scale Models 1 6 1 4 The scale factor is . This is reasonable because of the length of the model is 3 in. The length of the blueprint is 2, which is less. is less than . 1 6 1 4 Course 2 Insert Lesson Title Here Example #2 Identify the scale factor. blueprint length aircraft length 2 12 Write a ratio using one of the dimensions. = 1 6 = Simplify.

  6. 5-9 Scale Drawings and Scale Models Course 2 Example #3 A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is . Find the size of the photograph. 5 1 poster photo 5 1 = Think: 36 l 5 1 Write a proportion to find the length l. = 5l = 36 Find the cross products. l= 7.2 Divide.

  7. 5-9 Scale Drawings and Scale Models Course 2 Example #3 – cont. A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is . Find the size of the photograph. 5 1 poster photo 5 1 = Think: 20.5 w Write a proportion to find the width w. 5 1 = 5w = 20.5 Find the cross products. w= 4.1 Divide. The photo is 7.2 in. long and 4.1 in. wide.

  8. 5-9 Scale Drawings and Scale Models l 45 1.5 1 = Course 2 Example #4 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 . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 = Think: Write a proportion to find the length l. Find the cross products. l = 45 · 1.5 l= 67.5 Multiply.

  9. 5-9 Scale Drawings and Scale Models Course 2 Example #4 – cont. 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 . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 = Think: Write a proportion to find the width w. w 24 1.5 1 = w = 24 · 1.5 Find the cross products. w= 36 Multiply. The dollhouse is 67.5 inches long and 36 inches wide.

  10. 5-9 Scale Drawings and Scale Models Course 2 Example #5 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 60 7.5 d = Write a proportion. 1.5 · d = 60 · 7.5 Find the cross products. 1.5d = 450 Multiply. 450 1.5 1.5d 1.5 = Divide both sides by 1.5. d = 300 The distance between the cities is 300 miles.

  11. 5-9 Scale Drawings and Scale Models Course 2 Insert Lesson Title Here Example #5 – cont. 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 50 7 d = Write a proportion. Find the cross products. 1 · d = 50 · 7 1d = 350 Multiply. d = 350 The distance between the cities is 350 kilometers.

  12. 5-9 Scale Drawings and Scale Models 1 228 On a scale drawing, a kitchen wall is 6 inches long. The scale factor is . What is the length of the actual wall? 1 24 Course 2 Insert Lesson Title Here Concept Check Identify the scale factor. 1. 2.

  13. 5-9 Scale Drawings and Scale Models Course 2 Insert Lesson Title Here Concept Check - cont 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

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