Question

the volume of this cone is 1,610.82 cubic yards. 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 $V = 1610.82$ cubic - yards and $h=19$ yards.

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 $V = 1610.82$, $h = 19$ and $\pi\approx3.14$ into the formula:
\[

$$\begin{align*} r&=\sqrt{\frac{3\times1610.82}{3.14\times19}}\\ &=\sqrt{\frac{4832.46}{59.66}}\\ &=\sqrt{81}\\ & = 9 \end{align*}$$

\]

Answer:

$9$ yards