Question

the volume of this cone is 544.0992 cubic meters. what is the radius of this cone? round your answer to the nearest hundredth. 16 m r ≈ meters

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 $V = 544.0992$ cubic - meters and $h=16$ meters.

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

Step3: Substitute values and calculate

Substitute $V = 544.0992$, $h = 16$, and $\pi\approx3.14$ into the formula:
\[

$$\begin{align*} r&=\sqrt{\frac{3\times544.0992}{3.14\times16}}\\ &=\sqrt{\frac{1632.2976}{50.24}}\\ &=\sqrt{32.5}\\ &\approx5.70 \end{align*}$$

\]

Answer:

$5.70$