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.

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Accepted Answer

1. Volume of cylinder: $V_{cyl}=\pi R^2 h_{cyl}$.  
2. Volume of cone: $V_{cone}=\dfrac{1}{3}\pi R^2 h_{cone}$.  
3. Set equal: $\pi R^2 h_{cyl}=\dfrac{1}{3}\pi R^2 h_{cone}$, so $h_{cyl}=\dfrac{1}{3}h_{cone}$.  
4. Therefore the ratio $h_{cyl}:h_{cone}=1:3$.

FINAL_ANSWER: b

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