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 ≈ \boxed{} yards

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 \( \pi = 3.14 \). 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:

\( 12.00 \)