Question

determine the volume of the square based pyramid.

Explanation:

Step1: Recall volume formula

The volume formula for a square - based pyramid is $V=\frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height.

Step2: Find area of base

If the base has side length $s$, then $B = s^{2}$. Assume the side - length of the square base is $s$ and the height of the pyramid is $h$. From the problem, if we assume the side - length of the base is not given (but for a complete solution we would need it), let's assume the side - length of the base $s$ and height $h = 6$ cm. If we assume the base has side - length $s = 6$ cm, then $B=s^{2}=6\times6 = 36$ $cm^{2}$.

Step3: Calculate volume

Using the formula $V=\frac{1}{3}Bh$, substitute $B = 36$ $cm^{2}$ and $h = 6$ cm. So $V=\frac{1}{3}\times36\times6$. First, $\frac{1}{3}\times36 = 12$, then $12\times6=72$ $cm^{3}$.

Answer:

$72$ $cm^{3}$