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Volume of a Prism

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

Math diagram

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 $h$ .

$V = B h$

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

Example:

Find the volume of the prism shown.

Math diagram

Solution

The formula for the volume of a prism is $V = B h$ , 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 $A = l w$ .

So, the base area is $9 \times 7$ or $63 {cm}^{2}$ .

The height of the prism is $13$ cm.

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

$V = (63) (13)$

Multiply.

$V = 819$

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