Question

consider a cone with a height of 11 feet and a volume of 33π cubic feet. find the exact radius of the cone. be sure to use the correct unit in your answer. the radius of the cone is

Explanation:

Step1: Write the formula for the volume of a cone

The volume formula for a cone is \( V=\frac{1}{3}\pi r^{2}h \), where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

Step2: Substitute the given values into the formula

We know \( V = 33\pi\) and \( h=11 \). Substituting these into the formula gives \( 33\pi=\frac{1}{3}\pi r^{2}\times11 \).

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

First, cancel out \( \pi \) from both sides of the equation: \( 33=\frac{1}{3}r^{2}\times11 \). Then, multiply both sides by \( 3 \) to get \( 99 = 11r^{2} \). Next, divide both sides by \( 11 \): \( r^{2}=\frac{99}{11}=9 \).

Step4: Solve for \( r \)

Take the square root of both sides. Since \( r>0 \) (radius cannot be negative), \( r = \sqrt{9}=3 \).

Answer:

The radius of the cone is \( 3 \) feet.