Question

the volume of this cylinder is 3,165.12 cubic inches. what is the height? round your answer to the nearest hundredth. 12 in h h ≈ inches

Explanation:

Step1: Recall volume formula

The volume formula for a cylinder is $V=\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. Given radius $r = 12$ inches and $V=3165.12$ cubic - inches.

Step2: Rearrange formula for height

We can rewrite the formula for $h$ as $h=\frac{V}{\pi r^{2}}$.

Step3: Substitute values

Substitute $V = 3165.12$, $r = 12$ and $\pi\approx3.14$ into the formula: $h=\frac{3165.12}{3.14\times12^{2}}$. First, calculate $12^{2}=144$, then $3.14\times144 = 452.16$. So $h=\frac{3165.12}{452.16}$.

Step4: Calculate height

$h=\frac{3165.12}{452.16}=7.00$ inches.

Answer:

$7.00$