Question

A cone has a height of 9 inches and a diameter of 4 inches. Calculate the volume of the cone. (1 point)
Responses

36π in.3
36 pi in. cubed

48π in.3
48 pi in. cubed

12π in.3
12 pi in. cubed

27π in.3
27 pi in. cubed

Answer 1

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

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

where \( r \) is the radius of the base of the cone and \( h \) is the height of the cone.

Given:
- Height \( h = 9 \) inches
- Diameter \( = 4 \) inches, which means the radius \( r = \frac{4}{2} = 2 \) inches.

Now, we can substitute the values into the volume formula:

\[
V = \frac{1}{3} \pi (2^2)(9)
\]
\[
V = \frac{1}{3} \pi (4)(9)
\]
\[
V = \frac{1}{3} \pi (36)
\]
\[
V = 12\pi
\]

Therefore, the volume of the cone is \( 12\pi \) in³.

The correct response is:

**12π in.3 (12 pi in. cubed)**