Volume of a Prism

A prism is a polyhedron with two parallel, congruent faces called bases that are polygons.

The volume of a 3 -dimensional solid is the amount of space it occupies.  Volume is measured in cubic units ( in 3 , ft 3 , cm 3 , m 3 , et cetera).  Be sure that all of the measurements are in the same unit before computing the volume.

The volume V of a prism is the area of the base B times the height h .

V=Bh

Note: A cubic centimeter ( cm 3 ) is a cube whose edges measure 1 centimeter.

Example:

Find the volume of the prism shown.

Solution

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.

The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm.

The area A of a rectangle with length l and width w is A=lw .

So, the base area is 9×7 or 63 cm 2 .

The height of the prism is 13 cm.

Substitute 63 for B and 13 for h in V=Bh .

V=(63)(13)

Multiply.

V=819

Therefore, the volume of the prism is 819 cubic centimeters.