Question

the volume of this cylinder is 197.82 cubic millimeters. what is the radius? round your answer to the nearest hundredth.

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 $V = 197.82$ cubic - millimeters and $h = 7$ mm.

Step2: Rearrange formula for radius

We can rewrite the formula as $r^{2}=\frac{V}{\pi h}$. Substitute $V = 197.82$ and $h = 7$ into the formula: $r^{2}=\frac{197.82}{\pi\times7}$.

Step3: Calculate $r^{2}$

First, calculate $\frac{197.82}{\pi\times7}$. $\pi\approx3.14$, so $\frac{197.82}{3.14\times7}=\frac{197.82}{21.98}=9$.

Step4: Solve for $r$

Since $r^{2}=9$, then $r=\sqrt{9}= 3$ mm.

Answer:

3