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

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

Substituting the given values into the formula:

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

Calculating \( (12)^2 \):

\[
(12)^2 = 144
\]

Now substituting back into the formula:

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

Calculating \( 144 \times 18 \):

\[
144 \times 18 = 2592
\]

Now substituting this value back into the volume formula:

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

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

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

So, we have:

\[
V = 864 \pi
\]

For a numerical approximation, using \( \pi \approx 3.14 \):

\[
V \approx 864 \times 3.14 \approx 2711.76
\]

Thus, the volume of the cone is:

\[
\boxed{864\pi} \text{ cubic centimeters, or approximately } 2711.76 \text{ cubic centimeters.}
\]