Question

a cylinder has a height of 18 meters. its volume is 6,838.92 cubic meters. what is the radius of the cylinder? round your answer to the nearest hundredth. r ≈ meters

Explanation:

Step1: Recall the formula for the volume 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: Rearrange the formula to solve for \(r^{2}\)

We can rewrite the formula as \(r^{2}=\frac{V}{\pi h}\).
Substitute \(V = 6838.92\) cubic meters and \(h=18\) meters.
\(r^{2}=\frac{6838.92}{\pi\times18}\)
\(r^{2}=\frac{6838.92}{3.14\times18}\) (Take \(\pi = 3.14\))
\(r^{2}=\frac{6838.92}{56.52}\)
\(r^{2}=121\)

Step3: Solve for \(r\)

Take the square - root of both sides. \(r=\sqrt{121}\) or \(r = 11.00\) (since radius is non - negative)

Answer:

\(11.00\)