Volume of a Cone

A cone is to a cylinder what a pyramid is to a box. With the same base and the same height, a cone holds exactly a third of the cylinder.

This cone has radius 3, so its base circle has area $\pi\cdot {3}^{2} = 9\cdot \pi$. The cylinder with the same base and height 4 would hold $9\cdot \pi\cdot 4 = 36\cdot \pi$, and the cone holds a third of that: $12\cdot \pi$.

The rule is Volume of a cone: $V = \frac{1}{3}\cdot \pi\cdot {r}^{2}\cdot h$. Like the pyramid, it uses the true height, dashed inside the cone, never the slant height down its side.