Question

the volume of this cylinder is 2,034.72 cubic yards. what is the radius? round your answer to the nearest hundredth. 18 yd 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

Given \( V = 2034.72\) cubic yards and \( h=18\) yards. Substitute into \( V=\pi r^{2}h \):
\( 2034.72=\pi r^{2}\times18 \)

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

First, divide both sides by \( 18\pi \).
\( r^{2}=\frac{2034.72}{18\pi} \)
Take \( \pi = 3.14 \), then \( r^{2}=\frac{2034.72}{18\times3.14}=\frac{2034.72}{56.52}=36 \)

Step4: Solve for \( r \)

Take the square - root of both sides. \( r=\sqrt{36} = 6.00\)

Answer:

\(6.00\) yards