A cone has a radius of 12 centimeters and a height of 18 centimeters. What is the volume of the cone in cubic centimeters?

answers:

2,592 pi cm ^3

144pi cm^3

864 pi cm^3

1,296 pi cm^ 3

1 answer

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.

For the cone with a radius of \( 12 \) cm and a height of \( 18 \) cm, we can substitute these values into the formula:

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

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

\[ (12)^2 = 144 \]

Next, substitute \( 144 \) back into the volume formula:

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

Now, multiply \( 144 \) by \( 18 \):

\[ 144 \times 18 = 2592 \]

So the volume becomes:

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

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

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

Thus, the volume of the cone is:

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

Therefore, the answer is:

864 pi cm^3