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Scaling Three-Dimensional Figures 9-9 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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Scaling Three-Dimensional Figures 9-9 Warm Up Find the surface area of each rectangular prism. 1. length 14 cm, width 7 cm, height 7 cm 2. length 30 in., width 6 in., height 21 in 3. length 3 mm, width 6 mm, height 4 mm 4. length 37 in., width 9 in., height 18 in. 490 cm 2 1872 in 2 108 mm 2 2322 in 2

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Scaling Three-Dimensional Figures 9-9 Problem of the Day A model of a solid-steel machine tool is built to a scale of 1 cm = 10 cm. The real object will weigh 2500 grams. How much does the model, also made of solid steel, weigh? 2.5 g

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Scaling Three-Dimensional Figures 9-9 Prep for MA.8.G.5.1 …Convert units of measure between different measurement systems…and dimensions including…area…and derived units to solve problems. Rev MA.7.G.2.1 Sunshine State Standards

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Scaling Three-Dimensional Figures 9-9 Vocabulary capacity

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Scaling Three-Dimensional Figures 9-9

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Scaling Three-Dimensional Figures 9-9 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 2 3 = 8 times as large, and its surface area is 4 times as large as the 1 ft cube’s.

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Scaling Three-Dimensional Figures 9-9 Multiplying the linear dimensions of a solid by n creates n 2 as much surface area and n 3 as much volume. Helpful Hint

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Scaling Three-Dimensional Figures 9-9 A 3 cm cube is built from small cubes, each 1 cm on an edge. Compare the following values. the edge lengths of the two cubes Additional Example 1A: Scaling Models That Are Cubes 3 cm cube 1 cm cube 3 cm 1 cm Ratio of corresponding edges The length of the edges of the larger cube is 3 times the length of the edges of the smaller cube. = 3

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Scaling Three-Dimensional Figures 9-9 A 3 cm cube is built from small cubes, each 1 cm on an edge. Compare the following values. the surface areas of the two cubes Additional Example 1B: Scaling Models That Are Cubes 3 cm cube 1 cm cube 54 cm 2 6 cm 2 Ratio of corresponding areas The surface area of the large cube is 9 times that of the small cube. = 9

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Scaling Three-Dimensional Figures 9-9 A 3 cm cube is built from small cubes, each 1 cm on an edge. Compare the following values. the volumes of the two cubes Additional Example 1C: Scaling Models That Are Cubes 3 cm cube 1 cm cube 27 cm 3 1 cm 3 Ratio of corresponding volumes The volume of the large cube is 27 times that of the smaller cube. = 27

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Scaling Three-Dimensional Figures 9-9 An 8 cm cube is built from small cubes, each 2 cm on an edge. Compare the following values. the edge lengths of the two cubes Check It Out: Example 1A 8 cm cube 2 cm cube 8 cm 2 cm Ratio of corresponding edges The edges of the large cube are 4 times as long as the edges of the small cube. = 4

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Scaling Three-Dimensional Figures 9-9 A 8 cm cube is built from small cubes, each 2 cm on an edge. Compare the following values. the surface areas of the two cubes Check It Out: Example 1B 8 cm cube 2 cm cube 6(8 cm) 2 6(2 cm) 2 Ratio of corresponding areas The surface area of the large cube is 4 2 = 16 times that of the small cube. = 380 cm 2 24 cm 2 = 16

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Scaling Three-Dimensional Figures 9-9 A 8 cm cube is built from small cubes, each 2 cm on an edge. Compare the following values. the volumes of the two cubes Check It Out: Example 1C Ratio of corresponding volumes The volume of the large cube is 4 3 = 64 times that of the small cube. 8 cm cube 2 cm cube (8 cm) 3 (2 cm) 3 512 cm 3 8 cm 3 = 64

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Scaling Three-Dimensional Figures 9-9 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. What is the scale factor of the model? Additional Example 2A: Scaling Models That Are Other Solid Figures The scale factor of the model is. Convert and simplify. 1 8 6 in. 4 ft = 6 in. 48 in. = 1 8

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

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Scaling Three-Dimensional Figures 9-9 A box is in the shape of a rectangular prism. The box is 5 ft tall, and its base has a length of 6 ft and a width of 4 ft. For a 6 in. tall model of the box, find the following. the scale of the model? Check It Out: Example 2A The scale of the model is 1:10. 6 in. 5 ft 6 in. 60 in. = 1 10

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Scaling Three-Dimensional Figures 9-9 A box is in the shape of a rectangular prism. The box is 5 ft tall, and its base has a length of 6 ft and a width of 4 ft. For a 6 in. tall model of the box, find the following. the length and width of the model? Check It Out: Example 2B Length: 6 ft = in. 72 ft = 17 in. 1 10 1 1 2 Width: 4 ft = in. 48 ft = 4 in. 1 10 1 4 5

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Scaling Three-Dimensional Figures 9-9 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? Additional Example 3: Business Application V = 2 ft 2 ft 2 ft = 8 ft 3 Find the volume of the 2 ft cubic container. Set up a proportion and solve. Cancel units. 30 8 = x 240 = x It takes 240 seconds, or 4 minutes, to fill the larger container. Multiply. Calculate the fill time. 30 s 1 ft 3 x 8 ft 3 =

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Scaling Three-Dimensional Figures 9-9 It takes 8 s for a machine to fill a cubic box whose edge measures 4 cm. How long would it take to fill a cubic box whose edge measures 10 cm? Check It Out: Example 3 V smaller box = 4 cm 4 cm 4 cm = 64 cm 3 It would take 125 seconds, or 2 minutes 5 seconds, to fill. x s 1000 cm 3 = ; 8000 = 64x, so x = = 125 V larger box = 10 cm 10 cm 10 cm = 1000 cm 3 8 s 64 cm 3 8000 64

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Scaling Three-Dimensional Figures 9-9 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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Scaling Three-Dimensional Figures 9-9 A 10 cm cube is built from small cubes, each 1 cm on an edge. Compare the following values. 1. the edge lengths of the two cubes 2. the surface areas of the two cubes 3. the volumes of the two cubes Lesson Quiz: Part I 100:1 10:1 1000:1

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Scaling Three-Dimensional Figures 9-9 4. A pyramid has a square base measuring 185 m on each side and a height of 115 m. A model of it has a base 37 cm on each side. What is the height of the model? 5. A cement truck is pouring cement for a new 4 in. thick driveway. The driveway is 90 ft long and 20 ft wide. How long will it take the truck to pour the cement if it releases 10 ft 3 of cement per minute? Lesson Quiz: Part II 23 cm 60 min

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Scaling Three-Dimensional Figures 9-9 1. A 12 cm cube is built from small cubes, each 3 cm on an edge. Compare the edge lengths of the two cubes. A. 12:1 B. 6:1 C. 4:1 D. 3:1 Lesson Quiz for Student Response Systems

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Scaling Three-Dimensional Figures 9-9 2. A 20 cm cube is built from small cubes, each 5 cm on an edge. Compare the surface areas of the two cubes. A. 15:1 B. 16:1 C. 17:1 D. 18:1 Lesson Quiz for Student Response Systems

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Scaling Three-Dimensional Figures 9-9 3. The dimensions of a building are 140 m long, 125 m wide, and 200 m high. The scale model used to build the building is 14 cm long. What is the height of the model? A. 12.5 cm B. 20 cm C. 125 cm D. 200 cm Lesson Quiz for Student Response Systems

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Scaling Three-Dimensional Figures 9-9 4. An aquarium has dimensions 5 ft long, 4 ft wide, and 6 ft deep. How long will it take to fill the aquarium with water from a pipe which releases 2 ft 3 of water per minute? A. 15 min B. 30 min C. 45 min D. 60 min Lesson Quiz for Student Response Systems

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