Question

the volume of this cylinder is 7,959.9 cubic millimeters. what is the radius? round your answer to the nearest hundredth. 15 mm r ≈ millimeters

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. Given $V = 7959.9$ cubic - mm and $h = 15$ mm.

Step2: Rearrange the formula for radius

We can rewrite the formula as $r^{2}=\frac{V}{\pi h}$. Substitute $V = 7959.9$ and $h = 15$ into the formula: $r^{2}=\frac{7959.9}{\pi\times15}$.

Step3: Calculate $r^{2}$

First, calculate $\frac{7959.9}{\pi\times15}$. $\pi\approx3.14$, so $\frac{7959.9}{3.14\times15}=\frac{7959.9}{47.1}=169$.

Step4: Find the radius

Since $r^{2}=169$, then $r=\sqrt{169}$. So $r = 13.00$ mm.

Answer:

$13.00$