Question

a cylinder has a height of 2 yards. its volume is 25.12 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

Given \( V = 25.12\) cubic yards and \( h=2\) yards. Substitute into \( V=\pi r^{2}h \):
\( 25.12=\pi r^{2}\times2 \)

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

First, divide both sides by \( 2\pi \).
\( r^{2}=\frac{25.12}{2\pi} \). Using \( \pi\approx3.14 \), we have \( r^{2}=\frac{25.12}{2\times3.14}=\frac{25.12}{6.28} = 4 \)

Step4: Solve for \( r \)

Take the square root of both sides. \( r=\sqrt{4} = 2.00\)

Answer:

\(2.00\)