Question

a right circular cylinder has radius of 3 units and the volume 72π cubic units. what is the height of the cylinder?
√8 units
8 units
12 units
24 units

Explanation:

Step1: Recall volume formula

The volume formula for a right - circular cylinder is $V=\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height.

Step2: Substitute given values

We are given that $r = 3$ and $V=72\pi$. Substituting into the formula: $72\pi=\pi\times3^{2}\times h$.

Step3: Simplify the equation

First, simplify $3^{2}=9$. The equation becomes $72\pi = 9\pi h$. Divide both sides of the equation by $9\pi$. $\frac{72\pi}{9\pi}=h$.

Step4: Calculate the height

$\frac{72\pi}{9\pi}=8$, so $h = 8$.

Answer:

8 units