Question

the volume of this cylinder is 6,898.58 cubic yards. what is the radius? use π ≈ 3.14 and round your answer to the nearest hundredth. r ≈ yards 13 yd

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 $V = 6898.58$ cubic - yards, $h=13$ yards and $\pi\approx3.14$.

Step2: Rearrange the formula to solve for $r$

Starting from $V=\pi r^{2}h$, we can solve for $r^{2}$ first: $r^{2}=\frac{V}{\pi h}$. Then $r=\sqrt{\frac{V}{\pi h}}$.

Step3: Substitute the given values

Substitute $V = 6898.58$, $\pi\approx3.14$ and $h = 13$ into the formula for $r$. First, calculate $\frac{V}{\pi h}=\frac{6898.58}{3.14\times13}=\frac{6898.58}{40.82}=169$. Then $r=\sqrt{169}=13$ yards.

Answer:

13 yards