Question
A cone has a radius of 12 centimeters and a height of 18 centimeters. What is the volume of the cone in cubic centimeters?
Hint: The answer has pi
π in it, so you will not calculate that part. You will just include it at the end of the rest of your calculation.
pi "c" "m" cubed
pi "c" "m" cubed
pi "c" "m" cubed
pi "c" "m" cubed
Answers
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,
- \( h \) is the height.
Given:
- Radius (\( r \)) = 12 cm
- Height (\( h \)) = 18 cm
Now we can plug in the values:
\[
V = \frac{1}{3} \pi (12)^2 (18)
\]
Calculating \( (12)^2 \):
\[
(12)^2 = 144
\]
Now substituting back into the volume formula:
\[
V = \frac{1}{3} \pi (144)(18)
\]
Calculating \( 144 \times 18 \):
\[
144 \times 18 = 2592
\]
So now the volume is:
\[
V = \frac{1}{3} \pi (2592)
\]
Calculating \( \frac{2592}{3} \):
\[
\frac{2592}{3} = 864
\]
Thus, the volume of the cone is:
\[
V = 864 \pi \text{ cm}^3
\]
So the final answer is:
**864 π cm³**
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Given:
- Radius (\( r \)) = 12 cm
- Height (\( h \)) = 18 cm
Now we can plug in the values:
\[
V = \frac{1}{3} \pi (12)^2 (18)
\]
Calculating \( (12)^2 \):
\[
(12)^2 = 144
\]
Now substituting back into the volume formula:
\[
V = \frac{1}{3} \pi (144)(18)
\]
Calculating \( 144 \times 18 \):
\[
144 \times 18 = 2592
\]
So now the volume is:
\[
V = \frac{1}{3} \pi (2592)
\]
Calculating \( \frac{2592}{3} \):
\[
\frac{2592}{3} = 864
\]
Thus, the volume of the cone is:
\[
V = 864 \pi \text{ cm}^3
\]
So the final answer is:
**864 π cm³**