SOLUTION: A cone and a cylinder have the same radius and the same volume. Find the ratio of the height of the cone to the height of the cylinder.

Algebra ->  Surface-area -> SOLUTION: A cone and a cylinder have the same radius and the same volume. Find the ratio of the height of the cone to the height of the cylinder.       Log On


   

Question 1116876: A cone and a cylinder have the same radius and the same volume. Find the ratio of the height of the cone to the height of the cylinder.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For a cone,
V%5Bcone%5D=%28pi%2F3%29%2AR%5E2%2AH%5Bcone%5D
For a cylinder,
V%5Bcyl%5D=pi%2AR%5E2%2AH%5Bcyl%5D
So then,
V%5Bcone%5D=V%5Bcyl%5D
%28pi%2F3%29%2AR%5E2%2AH%5Bcone%5D=pi%2AR%5E2%2AH%5Bcyl%5D
%281%2F3%29%2AH%5Bcone%5D=H%5Bcyl%5D
H%5Bcone%5D%2FH%5Bcyl%5D=3