Question

A right cone and a right cylinder have the same radius and same height. What is the ratio of the volume of the cylinder to the volume of the cone
A) 3
B) 4
C) 6
D) 9

Answer 1

The volume of a right cone with radius $r$ and height $h$ is $\frac13\pi r^2h$, and the volume of a right cylinder with radius $r$ and height $h$ is $\pi r^2h$. The ratio of the volume of the cylinder to the volume of the cone is $\dfrac{\pi r^2h}{\dfrac13\pi r^2h}=\dfrac{\pi r^2h\cdot3}{\pi r^2h}=\boxed{3}$.