Section 8.2: Volumes of Cones

Property

A cone is a solid figure with one circular base and a vertex. For a cone with radius $r$ and height $h$:

Volume: $V = \frac{1}{3}\pi r^2 h$

Examples

• To find the volume of a cone with a height of 6 inches and a base radius of 2 inches, use $V = \frac{1}{3}\pi r^2 h$. With $\pi \approx 3.14$, the volume is $V \approx \frac{1}{3}(3.14)(2^2)(6) \approx 25.12$ cubic inches.

Property

A cone has exactly one-third the volume of a cylinder with the same base and height: $V_{cone} = \frac{1}{3} \cdot V_{cylinder}$

If cylinder volume is $V_{cylinder} = \pi r^2 h$, then cone volume is $V_{cone} = \frac{1}{3}\pi r^2 h$