### Home > MC2 > Chapter 11 > Lesson 11.3.1 > Problem11-85

11-85.

The area of the base in the prism below is $96$ square inches.

1. Find the volume of the prism.

Volume of a prism $=$ (area of base)(height)
Find the volume if the area of the base is $96$ square inches and the height is $25$ inches.

Volume = ($96$ in$^{2}$)($25$ in) $= 2400$ in$^{3}$

2. Find the volume of a pyramid with the same base and height.

The volume of a pyramid is $\frac{1}{3}$ the volume of a prism with the same base and height.

3. If another prism has the same volume as this prism, but its base area is $80$ square inches, what is its height?

Using the formula for volume of a prism,
$V =$ (area of base)(height) create an expression to solve for the height.

$2400 = (80)(\text{height})$

Height $= 30$ in