Question

a square pyramid has a height of 9 units and a volume of 147 units³. if a square prism has the same base area and volume as the square pyramid, what is its height? 1 unit 3 units 6 units 9 units

Explanation:

Step1: Find base - area of square pyramid

The volume formula for a square pyramid is $V=\frac{1}{3}Bh$, where $V$ is volume, $B$ is base - area and $h$ is height. Given $V = 147$ units³ and $h = 9$ units. We can solve for $B$:
$147=\frac{1}{3}B\times9$
$147 = 3B$
$B=\frac{147}{3}=49$ units².

Step2: Find height of square prism

The volume formula for a square prism is $V = Bh$. Since the volume of the square prism $V = 147$ units³ and base - area $B = 49$ units² (same as the pyramid's base - area), we solve for $h$:
$147=49h$
$h=\frac{147}{49}=3$ units.

Answer:

3 units