SOLUTION: Two similar cones have heights 5 and 20. What is the ratio of there volumes?

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Question 892414: Two similar cones have heights 5 and 20. What is the ratio of there volumes?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
volume of a cone, %281%2F3%29h%2Api%2Ar%5E2

If similar cones, then h and r of each are in proportion.
Compare %281%2F3%295pi%2Ar%5E2 to %281%2F3%2920%2Api%28%2820%2F5%29%28r%29%29%5E2=%281%2F3%2920%2Api%284r%29%5E2;
Notice that the larger cone has height 4 times larger and radius also 4 times larger.

Compare smaller volume to larger volume, ratio is %28%281%2F3%295pi%2Ar%5E2%29%2F%28%281%2F3%2920pi%284r%29%5E2%29

%285r%5E2%29%2F%2820%2A16%2Ar%5E2%29
%285cross%28r%5E2%29%29%2F%2820%2A16%2Across%28r%5E2%29%29
5%2F320
highlight%281%2F64%29