Question

The volume of a cone is 16 pi cubic inches. Its height is 12 inches. What is the radius of the cone?
2 in.
4 in.
12 in.
16 in.

Answer 1

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

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

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

Given that \( V = 16\pi \) cubic inches and \( h = 12 \) inches, we can substitute these values into the formula:

\[
16\pi = \frac{1}{3} \pi r^2 (12)
\]

We can simplify this equation. First, divide both sides by \( \pi \):

\[
16 = \frac{1}{3} r^2 (12)
\]

Now, simplify the right side:

\[
16 = 4 r^2
\]

Next, to isolate \( r^2 \), multiply both sides by \( \frac{1}{4} \):

\[
r^2 = 4
\]

Finally, take the square root of both sides to find \( r \):

\[
r = 2
\]

Thus, the radius of the cone is \( \boxed{2} \) inches.