Question

volume of a cone with radius of 12 height of 18

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

Now plug the values into the formula:

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

Calculating \( (12)^2 \):

\[
(12)^2 = 144
\]

Now, substitute this back into the volume formula:

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

Now calculate \( 144 \times 18 \):

\[
144 \times 18 = 2592
\]

Now substitute back:

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

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

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

Now, express the volume in terms of \( \pi \):

\[
V = 864 \pi
\]

Therefore, the volume of the cone is:

\[
V \approx 864 \times 3.14 \approx 2713.76
\]

So, the volume of the cone is \( 864 \pi \) cubic units, or approximately \( 2713.76 \) cubic units when using \( \pi \approx 3.14 \).