Question #4213

A cone has a radius of r units and a height of h units. A cylinder has a radius of 2r units and has the same volume as the cone. WHat is the height of the cylinder?

Expert's answer

The volume of the cone is equal to

V = 1/3 π r^{2} h

The volume of the cylinder is

V = π (2r)^{2} H

Thus

1/3 π r^{2} h = π 4r^{2} H

1/3 h = 4 H

H = 1/12 h

V = 1/3 π r

The volume of the cylinder is

V = π (2r)

Thus

1/3 π r

1/3 h = 4 H

H = 1/12 h

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