Question
A cone-shaped container on a farm is used for storing animal feed. The container has a radius of 4 feet and a height of 12 feet.(1 point)
The volume of feed, in cubic feet, this container can store is
The volume of feed, in cubic feet, this container can store is
Answers
GPT-4o mini
The volume \( V \) of a cone can be calculated using the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius of the base and \( h \) is the height of the cone.
Given:
- Radius \( r = 4 \) feet
- Height \( h = 12 \) feet
Using the formula:
\[
V = \frac{1}{3} \pi (4)^2 (12)
\]
Calculating \( (4)^2 \):
\[
(4)^2 = 16
\]
Now substituting back into the volume formula:
\[
V = \frac{1}{3} \pi (16) (12)
\]
Calculating \( 16 \times 12 \):
\[
16 \times 12 = 192
\]
Thus, the volume becomes:
\[
V = \frac{1}{3} \pi (192)
\]
Now dividing \( 192 \) by \( 3 \):
\[
\frac{192}{3} = 64
\]
So, the volume is:
\[
V = 64 \pi
\]
Approximating \( \pi \) as \( 3.14 \):
\[
V \approx 64 \times 3.14 = 200.96
\]
Therefore, the volume of feed the container can store is approximately \( 200.96 \) cubic feet, or exactly \( 64 \pi \) cubic feet.
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius of the base and \( h \) is the height of the cone.
Given:
- Radius \( r = 4 \) feet
- Height \( h = 12 \) feet
Using the formula:
\[
V = \frac{1}{3} \pi (4)^2 (12)
\]
Calculating \( (4)^2 \):
\[
(4)^2 = 16
\]
Now substituting back into the volume formula:
\[
V = \frac{1}{3} \pi (16) (12)
\]
Calculating \( 16 \times 12 \):
\[
16 \times 12 = 192
\]
Thus, the volume becomes:
\[
V = \frac{1}{3} \pi (192)
\]
Now dividing \( 192 \) by \( 3 \):
\[
\frac{192}{3} = 64
\]
So, the volume is:
\[
V = 64 \pi
\]
Approximating \( \pi \) as \( 3.14 \):
\[
V \approx 64 \times 3.14 = 200.96
\]
Therefore, the volume of feed the container can store is approximately \( 200.96 \) cubic feet, or exactly \( 64 \pi \) cubic feet.