Question

The height of a square pyramid is one half the length of each side. The volume of the pyramid is 972 in.3. What is the height of the pyramid?

Answer 1

The volume formula of a square pyramid is :

`V=(1)/(3)b^2h`

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 :

`\begin{gathered} 972=(1)/(3)b^2((b)/(2)) \\ 972=(1)/(6)b^3 \\ b^3=5832 \\ \sqrt[3]{b^3}=\sqrt[3]{5832} \\ b=18 \end{gathered}`

The height will be :

`\begin{gathered} h=(b)/(2)=(18)/(2) \\ h=9 \end{gathered}`

The answer is 9 inches