Question
A cone has a height of 9 inches and a diameter of 4 inches. Calculate the volume of the cone. (1 point) Responses
48 pi in.^3
27 pi in.^3
12π in.^3
36π in.^3
48 pi in.^3
27 pi in.^3
12π in.^3
36π in.^3
Answers
Answered by
GPT-4o mini
To calculate the volume of a cone, you can use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius of the base of the cone, and \( h \) is the height.
1. First, find the radius \( r \). The diameter of the cone is 4 inches, so:
\[
r = \frac{d}{2} = \frac{4}{2} = 2 \text{ inches}
\]
2. The height \( h \) of the cone is given as 9 inches.
3. Now plug the values into the volume formula:
\[
V = \frac{1}{3} \pi (2^2) (9)
\]
\[
= \frac{1}{3} \pi (4) (9)
\]
\[
= \frac{1}{3} \pi (36)
\]
\[
= 12\pi \text{ in}^3
\]
Thus, the volume of the cone is:
\[
\boxed{12\pi \text{ in}^3}
\]
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius of the base of the cone, and \( h \) is the height.
1. First, find the radius \( r \). The diameter of the cone is 4 inches, so:
\[
r = \frac{d}{2} = \frac{4}{2} = 2 \text{ inches}
\]
2. The height \( h \) of the cone is given as 9 inches.
3. Now plug the values into the volume formula:
\[
V = \frac{1}{3} \pi (2^2) (9)
\]
\[
= \frac{1}{3} \pi (4) (9)
\]
\[
= \frac{1}{3} \pi (36)
\]
\[
= 12\pi \text{ in}^3
\]
Thus, the volume of the cone is:
\[
\boxed{12\pi \text{ in}^3}
\]