Question

a cone has a radius of 6 feet and height of 18 feet. find the volume of the cone in terms of π. h = 18 ft. r = 6 ft. v = □π ft³

Explanation:

Step1: Recall the formula for the volume of a cone

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

Step2: Substitute the given values of \( r \) and \( h \) into the formula

We are given that \( r = 6 \) feet and \( h=18 \) feet. Substituting these values into the formula, we get:
\( V=\frac{1}{3}\pi\times(6)^{2}\times18 \)
First, calculate \( (6)^{2}=36 \). Then the expression becomes \( V = \frac{1}{3}\pi\times36\times18 \)

Step3: Simplify the expression

First, calculate \( \frac{1}{3}\times36 = 12 \). Then, multiply \( 12\times18 \):
\( 12\times18=216 \)
So, \( V = 216\pi \) cubic feet.

Answer:

\( 216 \)