Question

the volume of this cone is 4,121.25 cubic yards. what is the radius of this cone? round your answer to the nearest hundredth. 17.5 yd r ≈ yards

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. Given $V = 4121.25$ cubic - yards and $h=17.5$ yards.

Step2: Rearrange formula for radius

We can rewrite the volume formula to solve for $r$:
\[

$$\begin{align*} V&=\frac{1}{3}\pi r^{2}h\\ 3V&=\pi r^{2}h\\ r^{2}&=\frac{3V}{\pi h}\\ r&=\sqrt{\frac{3V}{\pi h}} \end{align*}$$

\]

Step3: Substitute values

Substitute $V = 4121.25$, $h = 17.5$ and $\pi\approx3.14$ into the formula for $r$:
\[

$$\begin{align*} r&=\sqrt{\frac{3\times4121.25}{3.14\times17.5}}\\ &=\sqrt{\frac{12363.75}{54.95}}\\ &=\sqrt{225} \end{align*}$$

\]

Step4: Calculate radius

$r = 15.00$ yards

Answer:

$15.00$ yards