A right circular cone and a hemisphere have equal base and equal volume. What is the ratio of the height of the cone to the radius of the hemisphere?

Explanation

Volume of cone = \frac{1}{3}\pi r^2 h. 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. This simplifies to h = 2r, so the ratio h:r is 2:1.

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