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Holt CA Course 1 10-7Scaling Three-Dimensional Figures Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures 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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Holt CA Course 1 10-7Scaling Three-Dimensional Figures MG2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor. California Standards

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures 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 cubes volume, or capacity, is 2 3 = 8 times as large, and its surface area is 2 2 = 4 times as large as the 1 ft cubes.

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures 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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Holt CA Course 1 10-7Scaling Three-Dimensional Figures 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 larger cube is 9 times that of the smaller cube. = 9

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures 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 larger cube is 27 times that of the smaller cube. = 27

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures A 2 cm cube is built from small cubes, each 1 cm on an edge. Compare the following values. the edge lengths of the large and small cubes Check It Out! Example 1A 2 cm cube 1 cm cube 2 cm 1 cm Ratio of corresponding edges The length of the edges of the larger cube is 2 times the length of the edges of the smaller cube. = 2

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures A 2 cm cube is built from small cubes, each 1 cm on an edge. Compare the following values. the surface areas of the two cubes Check It Out! Example 1B 2 cm cube 1 cm cube 24 cm 2 6 cm 2 Ratio of corresponding areas The surface area of the larger cube is 4 times that of the smaller cube. = 4

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures A 2 cm cube is built from small cubes, each 1 cm on an edge. Compare the following values. the volumes of the two cubes Check It Out! Example 1C 2 cm cube 1 cm cube 8 cm 3 1 cm 3 Ratio of corresponding volumes The volume of the larger cube is 8 times that of the smaller cube. = 8

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures The surface area of a box is 1300 in 2. What is the surface area of a similar box that is smaller by a scale factor of ? Additional Example 2A: Finding Surface Area and Volume of Similar Solids 1212 S = 1300 · 1212 2 = 1300 · 1414 = 325 in 2 Multiply by the square of the scale factor. Simplify the power. Multiply.

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures The volume of a childs swimming pool is 28 ft 3. What is the volume of a similar pool that is larger by a scale factor of 4? Additional Example 2B: Finding Surface Area and Volume of Similar Solids V = 28 · 4 3 Multiply by the cube of the scale factor. = 28 · 64 Simplify the power. = 1,792 ft 3 Multiply.

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures 1313 S = 1800 · 1313 2 = 1,800 · 1919 = 200 Multiply by the square of the scale factor. Simplify the power. Multiply. Check It Out! Example 2A The surface area of a box is 1800 in 2. Find the surface area of a smaller, similarly shaped box that has a scale factor of ?

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures Check It Out! Example 2B The volume of a small hot tub is 48 ft 3. What is the volume of a similar hot tub that is larger by a scale factor of 2? V = 48 · 2 3 Use the volume of the smaller prism and the cube of the scale factor. = 48 · 8 Simplify the power. = 384 ft 3 Multiply.

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures 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. 30 8 = x 240 = x It takes 240 seconds, or 4 minutes, to fill the larger container. Cross multiply. Calculate the fill time. 30 s 1 ft 3 x 8 ft 3 =

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures 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? Check It Out! Example 3 Set up a proportion and solve. V = 3 ft 3 ft 3 ft = 27 ft 3 Find the volume of the 3 ft cubic container. 30 27 = x 810 = x It takes 810 seconds, or 13.5 minutes, to fill the larger container. Cross multiply. Calculate the fill time. 30 s 1 ft 3 x 27 ft 3 = Set up a proportion and solve.

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Holt CA Course 1 10-7Scaling Three-Dimensional Figures 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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Holt CA Course 1 10-7Scaling Three-Dimensional Figures 4. The surface area of a prism is 600 ft 2. What is the surface area of a similar prism that is smaller by a scale factor of ? 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 66.7 ft 2 60 min 1313

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