The volume formula of a square pyramid is :
[tex]V=\frac{1}{3}b^2h[/tex]
Where b is the side of the square base
h is the height of the pyramid
From the problem, the volume of the pyramid is V = 972 in^3
the height is 1/2 of the base, so h = b/2
Using the formula above :
[tex]\begin{gathered} 972=\frac{1}{3}b^2(\frac{b}{2}) \\ 972=\frac{1}{6}b^3 \\ b^3=5832 \\ \sqrt[3]{b^3}=\sqrt[3]{5832} \\ b=18 \end{gathered}[/tex]
The height will be :
[tex]\begin{gathered} h=\frac{b}{2}=\frac{18}{2} \\ h=9 \end{gathered}[/tex]
The answer is 9 inches
