A cone and a hemisphere have equal bases and equal volumes. What is the ratio of the height of the cone to the radius of the hemisphere?

Explanation

Let the radius of the bases be r and the height of the cone be h. Volume of cone = \frac{1}{3}\pi r^2 h and Volume of hemisphere = \frac{2}{3}\pi r^3. Since they are equal, \frac{1}{3}\pi r^2 h = \frac{2}{3}\pi r^3 \implies h = 2r. The ratio is 2:1.

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