SOLUTION: a cone and a cylinder have the same diameters. How many times greater must the height of the cone be so that the two solids have the same volume? Explain.

Question 504853: a cone and a cylinder have the same diameters. How many times greater must the height of the cone be so that the two solids have the same volume? Explain.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Without loss of generality, suppose the diameter of the cone is 2 (e.g. radius = 1). Then the volume of the sphere is

and the volume of the cone is

Equating the two volumes, we see that h = 4; i.e. the height must be four times the radius, or twice the diameter.
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