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?

2,592pi cm ^ 3

144pi cm ^ 3

864pi cm ^ 3

1,296pi cm ^ 3

Answer 1

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 \( r = 12 \) cm
- Height \( h = 18 \) cm

We can substitute these values into the formula:

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

First, calculate \( (12)^2 \):

\[
(12)^2 = 144
\]

Now substitute it back into the volume formula:

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

Now calculate \( 144 \times 18 \):

\[
144 \times 18 = 2592
\]

Now substitute this value into the volume formula:

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

Now divide \( 2592 \) by \( 3 \):

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

So the volume is:

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

Therefore, the volume of the cone is:

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