Question

a cylinder has a height of 11 meters. its volume is 5,837.26 cubic meters. what is the radius of the cylinder?
round your answer to the nearest hundredth.
r ≈ meters

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 \( V = 5837.26\) cubic meters and \( h=11\) meters. Substituting into \( V=\pi r^{2}h \), we get \( 5837.26=\pi r^{2}\times11 \).

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

First, divide both sides of the equation by \( 11\pi \). \( r^{2}=\frac{5837.26}{11\pi} \). Using \( \pi\approx3.14 \), we have \( r^{2}=\frac{5837.26}{11\times3.14}=\frac{5837.26}{34.54} = 169 \).

Step4: Solve for \( r \)

Take the square root of both sides. \( r=\sqrt{169} = 13.00\) (since radius cannot be negative).

Answer:

\(13.00\) meters