Question

the volume of this cylinder is 4,363.90606 cubic inches. what is the radius? round your answer to the nearest hundredth.

Explanation:

Step1: Recall volume formula

The volume formula of a cylinder is $V=\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. We know $V = 4363.90606$ cubic - inches and $h=13.1$ inches.

Step2: Rearrange the formula for radius

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

Step3: Substitute values

Substitute $V = 4363.90606$, $h = 13.1$ and $\pi\approx3.14159$ into the formula: $r=\sqrt{\frac{4363.90606}{3.14159\times13.1}}$.
First, calculate the denominator: $3.14159\times13.1 = 41.154829$.
Then, $\frac{4363.90606}{41.154829}\approx106.0357$.
Finally, $r=\sqrt{106.0357}\approx10.30$.

Answer:

$10.30$