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: Recall volume formula for square - pyramid

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

Step2: Solve for base area $B$

Simplify the right - hand side of the equation: $\frac{1}{3}\times9B = 3B$. So, $3B=147$. Divide both sides by 3: $B=\frac{147}{3}=49$ units².

Step3: Recall volume formula for square - prism

The volume formula for a square - prism is $V = Bh$, where $V$ is the volume, $B$ is the base area, and $h$ is the height. Since the square - prism has the same volume ($V = 147$ units³) and base area ($B = 49$ units²) as the square - pyramid. We can find its height $h$ using the formula $h=\frac{V}{B}$.
$h=\frac{147}{49}$

Step4: Calculate the height of the square - prism

$\frac{147}{49}=3$ units.

Answer:

3 units