SOLUTION: the diameter of a sphere and the base of a cone is equal. what percentage of that diameter must the cones height be so that both volumes are equal?9

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Question 1093595: the diameter of a sphere and the base of a cone is equal. what percentage of that diameter must the cones height be so that both volumes are equal?9
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a sphere of radius r is %284%2F3%29%2Api%2Ar%5E2 .
The volume of a cone with radius r and height h is
%281%2F3%29%2Api%2Ar%5E2%2Ah .
If sphere and cone with same radius have the same volume,
%284%2F3%29%2Api%2Ar%5E3=%281%2F3%29%2Api%2Ar%5E2%2Ah .
That equation simplifies to
4r=h} <--> h=2%2Adiameter .
So the cone height needs to be twice the diameter.
That is highlight%28%22200%25%22%29 of the diameter.