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 = 1/3π r^2h)

Responses
A 2 ft
B 3 ft
C 4 ft
D 6 ft

1 answer

To find the radius of the cone, we can use the formula for the volume of a cone:

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

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

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

First, simplify the right side:

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

Next, we can divide both sides of the equation by \( \pi \):

\[ 18 = 2r^2 \]

Now, divide both sides by 2:

\[ 9 = r^2 \]

Finally, 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