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 π in it, so you will not calculate that part. You will just include it at the end of the rest of your calculation.
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 and \( h \) is the height of the cone.
Given:
- Radius \( r = 12 \) centimeters
- Height \( h = 18 \) centimeters
We start by calculating \( r^2 \):
\[
r^2 = 12^2 = 144
\]
Now substitute \( r^2 \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \pi (144)(18)
\]
Now calculate \( 144 \times 18 \):
\[
144 \times 18 = 2592
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \pi (2592)
\]
Finally, simplify the expression:
\[
V = \frac{2592}{3} \pi = 864 \pi
\]
Thus, the volume of the cone is:
\[
\boxed{864 \pi} \text{ cubic centimeters}
\]
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height of the cone.
Given:
- Radius \( r = 12 \) centimeters
- Height \( h = 18 \) centimeters
We start by calculating \( r^2 \):
\[
r^2 = 12^2 = 144
\]
Now substitute \( r^2 \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \pi (144)(18)
\]
Now calculate \( 144 \times 18 \):
\[
144 \times 18 = 2592
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \pi (2592)
\]
Finally, simplify the expression:
\[
V = \frac{2592}{3} \pi = 864 \pi
\]
Thus, the volume of the cone is:
\[
\boxed{864 \pi} \text{ cubic centimeters}
\]