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Volume of a Pyramid

A pyramid is a polyhedron with one base that is any polygon . Its other faces are triangles.

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 pyramid is one-third the area of the base $B$ times the height $h$ .

$V = \frac{1}{3} B h$

Example:

Find the volume of a regular square pyramid with base sides $10$ cm and altitude $18$ cm.

Solution

Draw a figure.

Math diagram

The formula for the volume of a pyramid is,

$V = \frac{1}{3} B h$

Since the base of the pyramid is a square, the base area is $10^{2}$ or $100 {cm}^{2}$ .

So, substitute $100$ for $B$ and $18$ for $h$ in the formula.

$\begin{array}{l} V = \frac{1}{3} (100) (18) \\ = 600 \end{array}$

Therefore, the volume of the square pyramid is $600 {cm}^{3}$ .