Question

the volume of this cylinder is 55,325.4812 cubic yards. what is the height? round your answer to the nearest hundredth. 28.3 yd h h ≈ yards

Explanation:

Step1: Recall volume formula for cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. We know $V = 55325.4812$ cubic - yards and $r=28.3$ yards.

Step2: Rearrange formula for height

We can rewrite the formula for $h$ as $h=\frac{V}{\pi r^{2}}$.

Step3: Substitute values

Substitute $V = 55325.4812$, $r = 28.3$ and $\pi\approx3.14159$ into the formula:
\[

$$\begin{align*} h&=\frac{55325.4812}{3.14159\times(28.3)^{2}}\\ &=\frac{55325.4812}{3.14159\times800.89}\\ &=\frac{55325.4812}{2516.477951}\\ &\approx22.0 \end{align*}$$

\]

Answer:

$22.00$ yards