Question

a cylinder has a radius of 16 yards. its volume is 8,038.4 cubic yards. what is the height of the cylinder?
round your answer to the nearest hundredth.
( h = square ) 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. We need to solve for \(h\), so we can rewrite the formula as \(h = \frac{V}{\pi r^{2}}\).

Step2: Substitute the given values into the formula

Given \(V = 8038.4\) cubic yards and \(r = 16\) yards. First, calculate \(r^{2}\): \(r^{2}=16^{2}=256\). Then substitute into the formula for \(h\): \(h=\frac{8038.4}{\pi\times256}\).

Step3: Calculate the value of \(h\)

We know that \(\pi\approx3.14\). So \(h=\frac{8038.4}{3.14\times256}\). First, calculate \(3.14\times256 = 803.84\). Then \(h=\frac{8038.4}{803.84}=10.00\)

Answer:

\(10.00\) yards