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Pre-Algebra

Learn to make scale models of solid figures. 7-9. Scaling Three-Dimensional Figures. Pre-Algebra. 7-9. Scaling Three-Dimensional Figures. Pre-Algebra. Helpful Hint. 7-9. Scaling Three-Dimensional Figures.

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Pre-Algebra

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  1. Learn to make scale models of solid figures. 7-9 Scaling Three-Dimensional Figures Pre-Algebra

  2. 7-9 Scaling Three-Dimensional Figures Pre-Algebra

  3. Helpful Hint 7-9 Scaling Three-Dimensional Figures Multiplying the linear dimensions of a solid by n creates n2 as much surface area and n3 as much volume. Pre-Algebra

  4. 3 cm cube 3 cm 7-9 Scaling Three-Dimensional Figures 1 cm cube 1 cm Pre-Algebra Example 1A: Scaling Models That Are Cubes A 3 cm cube is built from small cubes, each 1 cm on an edge. Compare the following values. A. the edge lengths of the large and small cubes Ratio of corresponding edges = 3 The edges of the large cube are 3 times as long as the edges of the small cube.

  5. 3 cm cube 54 cm2 7-9 Scaling Three-Dimensional Figures 1 cm cube 6 cm2 Pre-Algebra Example 1B: Scaling Models That Are Cubes B. the surface areas of the two cubes Ratio of corresponding areas = 9 The surface area of the large cube is 9 times that of the small cube.

  6. 3 cm cube 27 cm3 7-9 Scaling Three-Dimensional Figures 1 cm cube 1 cm3 Pre-Algebra Example 1C: Scaling Models That Are Cubes C. the volumes of the two cubes Ratio of corresponding volumes = 27 The volume of the large cube is 27 times that of the small cube.

  7. 7-9 Scaling Three-Dimensional Figures Pre-Algebra

  8. 7-9 Scaling Three-Dimensional Figures Pre-Algebra Corresponding edge lengths of any two cubes are in proportion to each other because the cubes are similar. However, volumes and surface areas do not have the same scale factor as edge lengths. Each edge of the 2 ft cube is 2 times as long as each edge of the 1 ft cube. However, the cube’s volume, or capacity, is 8 times as large, and its surface area is 4 times as large as the 1 ft cube’s.

  9. 1 6 in. 6 in. 7-9 Scaling Three-Dimensional Figures = = 8 4 ft 48 in. Pre-Algebra Example 2: Scaling Models That Are Other Solid Figures A box is in the shape of a rectangular prism. The box is 4 ft tall, and its base has a length of 3 ft and a width of 2 ft. For a 6 in. tall model of the box, find the following. A. What is the scale factor of the model? Convert and simplify. The scale factor of the model is 1:8.

  10. 1 24 36 1 1 1 7-9 Scaling Three-Dimensional Figures Width: 2 ft = in. = 3 in. Length: 3 ft = in. = 4 in. The length of the model is 4 in., and the width is 3 in. 8 8 8 2 8 2 Pre-Algebra Example 2B: Scaling Models That Are Other Solid Figures B. What are the length and the width of the model?

  11. x 30 s 7-9 Scaling Three-Dimensional Figures = 1 ft3 8 ft3 Pre-Algebra Example 3: Business Application It takes 30 seconds for a pump to fill a cubic container whose edge measures 1 ft. How long does it take for the pump to fill a cubic container whose edge measures 2 ft? Find the volume of the 2 ft cubic container. V = 2 ft  2 ft 2 ft = 8 ft3 Set up a proportion and solve. Cancel units. 30  8 = x Multiply. 240 = x Calculate the fill time. It takes 240 seconds, or 4 minutes, to fill the larger container.

  12. x 30 s 7-9 Scaling Three-Dimensional Figures = 1 ft3 27 ft3 Pre-Algebra Try This: Example 3 It takes 30 seconds for a pump to fill a cubic container whose edge measures 1 ft. How long does it take for the pump to fill a cubic container whose edge measures 3 ft? Find the volume of the 2 ft cubic container. V = 3 ft  3 ft 3 ft = 27 ft3 Set up a proportion and solve. 30  27 = x Multiply. 810 = x Calculate the fill time. It takes 810 seconds, or 13.5 minutes, to fill the larger container.

  13. 7-9 Scaling Three-Dimensional Figures Pre-Algebra

  14. 2 cm cube 2 cm 7-9 Scaling Three-Dimensional Figures 1 cm cube 1 cm Pre-Algebra Try This: Example 1A A 2 cm cube is built from small cubes, each 1 cm on an edge. Compare the following values. A. the edge lengths of the large and small cubes Ratio of corresponding edges = 2 The edges of the large cube are 2 times as long as the edges of the small cube.

  15. 2 cm cube 24 cm2 7-9 Scaling Three-Dimensional Figures 1 cm cube 6 cm2 Pre-Algebra Try This: Example 1B B. the surface areas of the two cubes Ratio of corresponding areas = 4 The surface area of the large cube is 4 times that of the small cube.

  16. 2 cm cube 8 cm3 7-9 Scaling Three-Dimensional Figures 1 cm cube 1 cm3 Pre-Algebra Try This: Example 1C C. the volumes of the two cubes Ratio of corresponding volumes = 8 The volume of the large cube is 8 times that of the small cube.

  17. 7-9 Scaling Three-Dimensional Figures Pre-Algebra Corresponding edge lengths of any two cubes are in proportion to each other because the cubes are similar. However, volumes and surface areas do not have the same scale factor as edge lengths. Each edge of the 2 ft cube is 2 times as long as each edge of the 1 ft cube. However, the cube’s volume, or capacity, is 8 times as large, and its surface area is 4 times as large as the 1 ft cube’s.

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