Question

Volume of a cone height 15 radius 6

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 of the base and \( h \) is the height of the cone.

Given:
- Height \( h = 15 \)
- Radius \( r = 6 \)

Substituting the values into the formula:

\[
V = \frac{1}{3} \pi (6^2)(15)
\]

Calculating \( 6^2 \):

\[
6^2 = 36
\]

Now substituting back:

\[
V = \frac{1}{3} \pi (36)(15)
\]

Calculating \( 36 \times 15 \):

\[
36 \times 15 = 540
\]

So, we have:

\[
V = \frac{1}{3} \pi (540)
\]

Calculating \( \frac{540}{3} \):

\[
\frac{540}{3} = 180
\]

Thus, the volume of the cone is:

\[
V = 180\pi
\]

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

\[
V \approx 180 \times 3.14 \approx 565.2
\]

So, the volume of the cone is \( 180\pi \) cubic units, or approximately \( 565.2 \) cubic units.