# A triangular pyramid and a triangular prism have the same base and height. The volume of the prism is how many times the volume of the pyramid?

## I don't know what it means.

Apr 20, 2018

The volume of the prism is three times that of the volume of the pyramid.

#### Explanation:

Let ${V}_{p y r}$ = the volume of the pyramid.

Let ${V}_{p r i s}$ = the volume of the prism.

We know that

${V}_{p y r} = \frac{1}{3} \times$ area of base $\times$ height

and

${V}_{p r i s} =$ area of base $\times$ height

The problem is asking for the ratio

${V}_{p r i s} / {V}_{p y r} = \frac{1}{\frac{1}{3}} = 3$

because the area of the base and the height cancel out.