Similarity in Two- and Three-Dimensional Figures Problem Set

Throughout this topic, you learned how to determine if two- and three-dimensional figures are similar. Now it is time for you to apply your knowledge in this assignment. Answer all of the questions below and make sure to show all of your work.

1. What is the ratio of the surface areas of two similar spheres if their scale factor is 5:6?
2. What is the ratio of the volumes of two similar prisms if the ratio of their perimeters is 4:11?
3. The ratio of the volumes of two similar cylinders is 343:1728. Find the ratio of their areas.
4. Two similar prisms have a lateral area ratio of 64:169. Find the ratio of their volumes.
   
5. The ratio of the perimeters of two similar triangular prisms is 3:8. If the area of the smaller prism is 84 cm², what is the area of the larger prism? Round your answer to the nearest tenth.
6. The ratio of the heights of two similar pyramids is 5:9. If the volume of the larger pyramid is 1,750 ft³, what is the volume of the smaller pyramid? Round your answer to the nearest tenth.
7. The ratio of the lateral areas of two similar rectangular prisms is 36:49. If the volume of the smaller rectangular prism is 737 km³, find the volume of the smaller one. Round your answer to the nearest tenth.
8. The ratio of the volumes of two similar cubes is 64:125. If the surface area of the larger cube is 327 mm², find the surface area of the smaller cube. Round your answer to the nearest tenth.
   

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