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 in it, so you will not calculate that part.
You will just include it at the end of the rest of your calculation.
π
2,592π cm
3
144π cm
3
864π cm
3
1,296 π cm
3

Answer 1

To find the volume of the cone, we can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( r \) is the radius and \( h \) is the height.

Given:
- Radius \( r = 12 \) cm
- Height \( h = 18 \) cm

Now, substituting these values into the formula:

\[
V = \frac{1}{3} \pi (12)^2 (18)
\]

Calculating \( (12)^2 \):

\[
(12)^2 = 144
\]

Now substituting this back into the formula:

\[
V = \frac{1}{3} \pi (144)(18)
\]

Calculating \( 144 \times 18 \):

\[
144 \times 18 = 2592
\]

Now substitute that back in:

\[
V = \frac{1}{3} \pi (2592)
\]

Calculating \( \frac{2592}{3} \):

\[
\frac{2592}{3} = 864
\]

Thus, the volume of the cone is:

\[
V = 864 \pi \, \text{cm}^3
\]

So the volume of the cone is \( \boxed{864 \pi \, \text{cm}^3} \).