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 formula for the volume \( V \) of a cone is given by:

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

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

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

Now, substituting the values into the formula:

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

Calculating \( (12)^2 \):

\[
12^2 = 144
\]

Now substitute this value back into the volume formula:

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

Next, calculate \( 144 \times 18 \):

\[
144 \times 18 = 2592
\]

Now substitute this product back into the volume formula:

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

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

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

Thus, the volume of the cone is:

\[
V = 864 \pi
\]

If you want a numerical approximation, you can use \( \pi \approx 3.14 \):

\[
V \approx 864 \times 3.14 \approx 2710.56
\]

Therefore, the volume of the cone is:

\[
\text{Exact volume: } 864 \pi \ \text{cubic centimeters} \quad \text{or approximately } 2710.56 \ \text{cubic centimeters.}
\]