Question

a cylinder has a height of 17 yards. its volume is 21,352 cubic yards. what is the radius of the cylinder?
round your answer to the nearest hundredth.
r ≈ yards

Explanation:

Step1: Write the formula for the volume of a cylinder

The volume formula for 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 \(V = 21352\) cubic yards and \(h=17\) yards. So, \(21352=\pi r^{2}\times17\).

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

First, divide both sides of the equation by \(17\pi\). \(r^{2}=\frac{21352}{17\pi}\).
Since \(\pi\approx3.14\), then \(r^{2}=\frac{21352}{17\times3.14}=\frac{21352}{53.38}\approx400\).

Step4: Solve for \(r\)

Take the square - root of both sides. \(r=\sqrt{400}\approx20.00\) (because we are asked to round to the nearest hundredth and \(\sqrt{400} = 20\)).

Answer:

\(20.00\) yards