Question
A popcorn container is the shape of an inverted cone. It is 9 inches tall, and the circular opening has a diameter of 4 inches. Which equation can be used to find the volume of the container?
V = one-third pi (2) squared (9)
V = one-third pi (4) squared (9)
V = one-third pi (4) (9) squared
V = one-third pi (2) (9) squared
V = one-third pi (2) squared (9)
V = one-third pi (4) squared (9)
V = one-third pi (4) (9) squared
V = one-third pi (2) (9) squared
Answers
GPT-4o mini
To find the volume \( V \) of a cone, you can use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.
In this case, the diameter of the circular opening is 4 inches, which means the radius \( r \) is:
\[
r = \frac{d}{2} = \frac{4}{2} = 2 \text{ inches}
\]
The height \( h \) of the cone is given as 9 inches.
Now we can substitute the values for \( r \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \pi (2)^2 (9)
\]
Calculating \( (2)^2 \):
\[
V = \frac{1}{3} \pi (4) (9)
\]
Therefore, the correct equation to find the volume of the container is:
\[
V = \frac{1}{3} \pi (4) (9)
\]
So, the correct answer is:
**V = one-third pi (4) squared (9)**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.
In this case, the diameter of the circular opening is 4 inches, which means the radius \( r \) is:
\[
r = \frac{d}{2} = \frac{4}{2} = 2 \text{ inches}
\]
The height \( h \) of the cone is given as 9 inches.
Now we can substitute the values for \( r \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \pi (2)^2 (9)
\]
Calculating \( (2)^2 \):
\[
V = \frac{1}{3} \pi (4) (9)
\]
Therefore, the correct equation to find the volume of the container is:
\[
V = \frac{1}{3} \pi (4) (9)
\]
So, the correct answer is:
**V = one-third pi (4) squared (9)**.