Question

The volume of a cone is 18π cubic feet. If the height of the cone is 6 ft, what is the radius of the cone? (V =





π
h)
Responses
A 2 ft2 ft
B 3 ft3 ft
C 4 ft4 ft
D 6 ft

Answer 1

The formula for the volume \(V\) of a cone is given by:

\[
V = \frac{1}{3} \pi r^2 h
\]

Where:
- \(r\) is the radius of the base of the cone,
- \(h\) is the height of the cone.

We know that the volume \(V = 18\pi\) cubic feet and the height \(h = 6\) ft. We can plug these values into the formula and solve for \(r\):

\[
18\pi = \frac{1}{3} \pi r^2 (6)
\]

First, simplify the equation:

\[
18\pi = 2\pi r^2
\]

Now, divide both sides by \(\pi\):

\[
18 = 2r^2
\]

Next, divide both sides by 2:

\[
9 = r^2
\]

Now, take the square root of both sides:

\[
r = 3
\]

Thus, the radius of the cone is \(3\) ft.

The correct response is **B**: 3 ft.