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A cylinder and a cone have the same base radius and the same volume. What is the ratio of the height of the cylinder to the height of the cone?

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

Correct answer: 1:3

Solution

Volume of cylinder = \(\pi r^2 h_c\) and volume of cone = \(\frac{1}{3}\pi r^2 h_k\). With equal volumes and same radius, \(h_c = \frac{1}{3}h_k\), so the ratio of cylinder height to cone height is 1:3.

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