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

Let the base radius and height be $\mathrm{r}$ and $\mathrm{h}$ respectively.

Volume of a cone $=\frac{1}{3}\pi {\mathrm{r}}^2\mathrm{h}$

Volume of a cylinder $=\pi {\mathrm{r}}^2\mathrm{h}$

Therefore, the ratio of the volume of the cylinder to the volume of the cone $=\frac{{\mathrm{\pi r}}^2\mathrm{h}}{{\displaystyle \frac{1}{3}}{\mathrm{\pi r}}^2\mathrm{h}}=\mathbf{3}\mathbf{:}\mathbf{1}$