Question

the volume of this cone is 112.84218 cubic inches. 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. We know $V = 112.84218$ cubic - inches and $h=9.9$ inches.

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 $\pi h$: $r^{2}=\frac{3V}{\pi h}$. Taking the square - root of both sides gives $r=\sqrt{\frac{3V}{\pi h}}$.

Step3: Substitute values and calculate

Substitute $V = 112.84218$, $h = 9.9$ and $\pi\approx3.14159$ into the formula:
\[

$$\begin{align*} r&=\sqrt{\frac{3\times112.84218}{3.14159\times9.9}}\\ &=\sqrt{\frac{338.52654}{31.001741}}\\ &=\sqrt{10.92}\\ &\approx3.30 \end{align*}$$

\]

Answer:

$3.30$ inches