If a cone and a cylinder have the same base and the same height, then the volume of the cone is $\frac{1}{3}$ of the volume of the cylinder.

For example, the cylinder and cone shown here both have a height of 7 feet and a base with radius 3 feet.

The cylinder has a volume of $63\pi$ cubic feet since $\pi \boldcdot 3^2 \boldcdot 7 = 63\pi$.

The cone has a volume that is $\frac13$ of that, or $21\pi$ cubic feet.

If the radius for both solids is $r$ and the height for both solids is $h$, then the volume of the cylinder is $\pi r^2h$. That means that the equation to give the volume, $V$, of the cone is $\displaystyle V=\frac{1}{3}\pi r^2h.$