Question

the volume of this cone is 452.16 cubic millimeters. what is the radius of this cone? round your answer to the nearest hundredth.

Explanation:

Step1: Recall volume formula for cone

The volume formula of a cone is $V = \frac{1}{3}\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. Given $V = 452.16$ cubic - millimeters and $h=12$ mm.

Step2: Rearrange formula to solve for $r$

Starting from $V=\frac{1}{3}\pi r^{2}h$, we can first multiply both sides by 3 to get $3V=\pi r^{2}h$. Then divide both sides by $\pi h$: $r^{2}=\frac{3V}{\pi h}$. Substitute $V = 452.16$, $h = 12$ and $\pi\approx3.14$ into the formula.
$r^{2}=\frac{3\times452.16}{3.14\times12}$

Step3: Calculate the value of $r^{2}$

$\frac{3\times452.16}{3.14\times12}=\frac{1356.48}{37.68}=36$

Step4: Solve for $r$

Since $r^{2}=36$, then $r=\sqrt{36}=6$ mm

Answer:

6.00