Question

A square pyramid has volume 324 cm^3. If the height of the pyramid is 12 cm, what is the length of each side of the square base?

Answer 1

ANSWER

9cm

EXPLANATION

The volume of a square pyramid is calculated using the formula;

$V = \frac{1}{3} {l}^{2}h$

where h=12cm is the height of the pyramid and l is the length of each side of the square base.

The volume is V=324.

We substitute the values in to the formula and solve for l.

$324 = \frac{1}{3} {l}^{2} \times 12$

$324 = 1 {l}^{2}$

${l}^{2} = \frac{324}{4}$

${l}^{2} = 81$

$l = \sqrt{81} = 9$

The length of each side of the square base is 9 cm.