Question

volume of the cone with radius of 5 and height of 9

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 of the base of the cone,
- \( h \) is the height of the cone.

Given that the radius \( r = 5 \) and the height \( h = 9 \), we can substitute these values into the formula:

\[
V = \frac{1}{3} \pi (5)^2 (9)
\]

Now, calculate \( (5)^2 \):

\[
(5)^2 = 25
\]

So the volume equation becomes:

\[
V = \frac{1}{3} \pi (25)(9)
\]

Now calculate \( 25 \times 9 = 225 \):

\[
V = \frac{1}{3} \pi (225)
\]

Now divide \( 225 \) by \( 3 \):

\[
\frac{225}{3} = 75
\]

Thus the volume is:

\[
V = 75\pi
\]

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

\[
V \approx 75 \times 3.14 \approx 235.5
\]

So the volume of the cone is \( 75\pi \) cubic units, or approximately \( 235.5 \) cubic units.