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 27π in.3 27 pi in. cubed 12π in.3 12 pi in. cubed 48π in.3 48 pi in. cubed
Answers
GPT-4o mini
To calculate the volume of a cone, we can use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given:
- Height (\( h \)) = 9 inches
- Diameter = 4 inches, so the radius (\( r \)) is half of the diameter: \( r = \frac{4}{2} = 2 \) inches.
Now, substituting the values of \( r \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \pi (2)^2 (9)
\]
\[
= \frac{1}{3} \pi (4) (9)
\]
\[
= \frac{1}{3} \pi (36)
\]
\[
= 12\pi \text{ cubic inches}
\]
Thus, the volume of the cone is \( 12\pi \) cubic inches.
The correct answer is:
**12π in.³** (or **12 pi in. cubed**)
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given:
- Height (\( h \)) = 9 inches
- Diameter = 4 inches, so the radius (\( r \)) is half of the diameter: \( r = \frac{4}{2} = 2 \) inches.
Now, substituting the values of \( r \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \pi (2)^2 (9)
\]
\[
= \frac{1}{3} \pi (4) (9)
\]
\[
= \frac{1}{3} \pi (36)
\]
\[
= 12\pi \text{ cubic inches}
\]
Thus, the volume of the cone is \( 12\pi \) cubic inches.
The correct answer is:
**12π in.³** (or **12 pi in. cubed**)