Question

A cone and a hemisphere has good bases and equal volume find the ratio of their heights

Answer 1

Since the cone and the hemisphere have the same base their radii are equal. We will take it as r units.

Let the height of the cone be h. The hemisphere is of height = radius r.

Given volume of the cone = volume of the hemisphere.

So (1/3) π r^2 h = (2/3) πr^3

Simplifying h = 2r or h:r = 2:1

Ratio of the heights of the cone and hemisphere = 2:1

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