Question

a cylinder has a height of 13 yards. its volume is 5,878.08 cubic yards. what is the radius of the cylinder? use π ≈ 3.14 and round your answer to the nearest hundredth. r ≈ □ yards submit

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by the formula \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. We know \( V = 5878.08 \) cubic yards, \( h=13 \) yards and \( \pi\approx3.14 \). We need to solve for \( r \).

First, we can rearrange the formula to solve for \( r^{2} \):
\( r^{2}=\frac{V}{\pi h} \)

Step2: Substitute the known values into the formula for \( r^{2} \)

Substitute \( V = 5878.08 \), \( \pi=3.14 \) and \( h = 13 \) into the formula:
\( r^{2}=\frac{5878.08}{3.14\times13} \)

First, calculate the denominator: \( 3.14\times13 = 40.82 \)

Then, calculate the numerator divided by the denominator: \( \frac{5878.08}{40.82}=144 \)

Step3: Solve for \( r \)

Now that we have \( r^{2}=144 \), we take the square root of both sides to find \( r \):
\( r=\sqrt{144} = 12.00 \) (since radius is a non - negative quantity, we take the positive square root)

Answer:

\( 12.00 \)