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Lesson 23T ~ Similar Solids Name__________________________________________ Period______ Date____________ Determine if each pair of solids is similar. Write each ratio as a fraction. 1. a. Ratio of the lengths: 10 b. Ratio of the widths: 5 4 c. Ratio of the heights: 2 4 8 d. Are the ratios all the same? Yes No e. Are the prisms similar? Yes No 6 2. a. What is the ratio of the radii? 8 b. What is the ratio of the heights? 8 c. Are the ratios the same? Yes No d. Are the cylinders similar? Yes No 12 Circle the correct answer. 3. The scale factor between Solid A and Solid B is 3 : 4. What is the ratio between their heights? A. 3 : 4 B. 9 : 16 C. 27 : 64 4. The scale factor between Solid T and Solid Y is 1 : 2. Identify their area ratio. A. 1 : 2 B. 1 : 4 C. 1 : 8 5. The scale factor between Solid Q and Solid M is 2 : 5. Identify the area ratio. A. 2 : 5 B. 4 : 25 C. 8 : 125 6. The ratio between the diameters of two similar cylinders is a : b. What is the volume ratio between the two cylinders? A. a : b ©2008 SMC Curriculum B. a² : b² C. a³ : b ³ Oregon Focus on Surface Area and Volume 7. Two similar prisms have a scale factor of 1 : 3. The small prism has a volume of 250 mm³. Find the volume of the large prism. a. Find the volume ratio. a³ : b³ → 1³ : 3³ → b. Write the volume ratio as a fraction. c. Which ratio below can be used to find the volume of the large prism? 1 250 3 x or 1 250 27 x d. Set the cross products equal to one another. e. What is the volume of the large prism? 8. A large wooden board has an area of 200 in². A small wooden board is similar to the large one. The ratio of their lengths is 2 : 1. Find the area of the small board. a. Find the ratio of their areas. b. Write a proportion to find the area of the small board. c. Find the area of the small board. 9. Two cylinders have a scale factor of 3 : 2. The surface area of the small cylinder is 43 ft². Find the surface area of the large cylinder. ©2008 SMC Curriculum Oregon Focus on Surface Area and Volume