SOLUTION: A solid metal cylinder of radius 6 cm and height 18 cm is melted down and recast as a cone of radius 6 cm. What is the height of the cone?

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Question 80753: A solid metal cylinder of radius 6 cm and height 18 cm is melted down and recast as a cone of radius 6 cm. What is the height of the cone?
Answer by ankor@dixie-net.com(12695) About Me  (Show Source):
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A solid metal cylinder of radius 6 cm and height 18 cm is melted down and recast as a cone of radius 6 cm. What is the height of the cone?
:
Vol of cyl = pi%2Ar%5E2%2Ah
Vol of cone = %28pi%2Ar%5E2%2Ah%29%2F3
:
An easy way to do this:
Cone Vol = Cylinder Vol
%28pi%2A6%5E2%2Ah%29%2F3 = pi%2A6%5E2%2A18
:
Divide both sides by pi%2A6%5E2; you have
h%2F3 = 18
:
h = 18 * 3
h = 54 is height of the cone