Question

the volume of this cylinder is 9,184.5 cubic yards. what is the radius? round your answer to the nearest hundredth. 13 yd r = yards submit

Explanation:

Step1: Recall the volume formula of a cylinder

The volume formula of a cylinder is \(V=\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.

Step2: Substitute the given values into the formula

We know that \(V = 9184.5\) cubic yards and \(h=13\) yards. Substituting these into the formula gives \(9184.5=\pi r^{2}\times13\).

Step3: Solve for \(r^{2}\)

First, divide both sides of the equation by \(13\pi\). \(\pi\approx3.14\), so \(r^{2}=\frac{9184.5}{13\times3.14}\).

$$r^{2}=\frac{9184.5}{40.82}$$

$$r^{2}=225$$

Step4: Solve for \(r\)

Take the square root of both sides. \(r=\sqrt{225}\) (we consider the positive root since radius is non - negative). But wait, let's do it more accurately with the formula.

$$r=\sqrt{\frac{V}{\pi h}}$$

$$r=\sqrt{\frac{9184.5}{3.14\times13}}$$

$$r=\sqrt{\frac{9184.5}{40.82}}$$

$$r=\sqrt{225}$$

$$r = 15.00$$

Answer:

\(15.00\) yards