Similar Solids
The surface areas of two similar rectangular prisms are 361m2 and 441m2 What is the scale factor of the larger prism to the smaller prism?
NOT A.
The two cylinders are similar. If the ratio of their surface areas is 9/1.44, find the volume of each cylinder. Round your answer to the nearest hundredth.
NOT B. small cylinder: 972.14 m3 large cylinder: 12,924.24 m3
2004-06-01-07-00_files/i0320000.jpg The triangular prisms are similar. Find the volume of the larger prism. Round your answer to the nearest hundredth.
NOT C. 88.16 in.3
2004-06-01-07-00_files/i0060000.jpg The two cones above are similar. Find the scale factor and the ratio of the surface areas.
NOT C. scale factor: 3/5 surface area ratio:9/25
The two cones are similar. The ratio of their surface areas is 13.69/4. Find the volume of each cone. Round your answer to the nearest hundredth.
NOT C. small cone: 432.32m2 large cone: 2,738.82m2
2004-06-01-07-00_files/i0310000.jpg The square pyramids are similar. Find the volume of the smaller pyramid. Round your answer to the nearest hundredth.
NOT D. 4.68 yd3
2004-06-01-07-00_files/i0020000.jpg Find the ratio of the surface areas of the solids.
Not C. 2/3
The two square pyramids are similar. Find the total volume of both pyramids if the ratio of their surface areas is 9/16.
B. 546in.3
2004-06-01-07-00_files/i0330000.jpg The cylinders are similar. Find the volume of the smaller cylinder. Round your answer to the nearest hundredth.
D. 153.24ft3
The surface areas of two similar solids are 450mm3 and 578mm3. If the volume of the smaller solid is 511mm3, find the volume of the larger solid. Round your answer to the nearest hundredth.
D. 743.86mm3
A museum has a 1/1000 scale model of the Grand Canyon, complete with a miniature river in the bottom. Explain how you could use the model to approximate the volume of water in the Grand Canyon.
The scale factor is 1:1000, which means the volume ratio of the model to the actual Grand Canyon is 1:1000^3, or 1:1,000,000,000. This ratio applies to the volume of the canyon and model as a whole, but it also applies to any part of the model and actual canyon, such as the river in the bottom. So there is 1,000,000,000 times more water in the actual canyon as in the model. Measuring the volume of water in the model and multiplying by 1,000,000,000 would allow you to approximate the volume of water in the canyon.