Similar Solids Worksheet
A Grade 12 Math worksheet focusing on the properties and calculations related to similar solids, including ratios of corresponding linear measures, areas, and volumes.
Includes
Standards
Similar Solids: Ratios and Proportions
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Read each question carefully and answer to the best of your ability. Show all work for calculations.
1. If two solids are similar and the ratio of their corresponding linear measures is a:b, what is the ratio of their surface areas?
a:b
a²:b²
a³:b³
√a:√b
2. Two similar cones have volumes of 27π cm³ and 64π cm³. What is the ratio of their heights?
3:4
9:16
27:64
√27:√64
3. If the ratio of the surface areas of two similar pyramids is 4:25, then the ratio of their corresponding slant heights is .
4. Two similar spheres have radii in the ratio of 1:3. The volume of the larger sphere is 270 cm³. The volume of the smaller sphere is cm³.
5. A small cube has a side length of 3 cm. A larger cube is similar to the small cube and has a side length of 9 cm. Calculate the ratio of their volumes. Show your work.
6. All cubes are similar solids.
True
False
7. If two solids have the same volume, they must be similar.
True
False
8. Two similar cylindrical water tanks have heights of 4 meters and 10 meters, respectively. If the smaller tank can hold 3200 liters of water, how many liters can the larger tank hold?