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A cylinder and a cone have the same base radius \(R\) and the same volume. Determine the ratio of the height of the cylinder to the height of the cone.

1. 3:1
2. 1:3
3. 2:3
4. 3:2

Correct answer: 1:3

Solution

Since the base radius is the same, the base area is the same. Equal volumes give \(\pi R^2 h_{cyl} = \frac{1}{3}\pi R^2 h_{cone}\), so \(h_{cyl} = \frac{1}{3}h_{cone}\). Therefore, the ratio is 1:3.

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