Question

what is the formula for the volume of a cone?
a. $2\pi r^{2}h$
b. $\frac{1}{3}\pi rh^{2}$
c. $\pi r^{2}h$
d. $\frac{1}{3}\pi r^{2}h$

Explanation:

Step1: Recall the volume formula of a cylinder

The volume formula of a cylinder is $V = \pi r^{2}h$, where $r$ is the radius of the base and $h$ is the height.

Step2: Consider the relationship between a cone and a cylinder

A cone with the same base radius $r$ and height $h$ as a cylinder has a volume that is one - third of the volume of the cylinder.
So the volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$.

Answer:

D. $\frac{1}{3}\pi r^{2}h$