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

The cylinder's volume is $\pi r^2 h$ and the cone's volume is $\frac{1}{3}\pi r^2 h$. With the same radius and height, the factor $\pi r^2 h$ cancels in the ratio: $\frac{\pi r^2 h}{\frac{1}{3}\pi r^2 h} = 3$. So the ratio of cylinder to cone is $3:1$, choice B. Equivalently, three cones of water fill one cylinder. Choice A (1:3) is the ratio in the opposite order, cone to cylinder. Choice C (1:1) ignores the $\frac{1}{3}$ in the cone's formula. Choice D (2:1) has no basis; it would apply to a hemisphere compared with a cone of the same size, not this pair of solids.