Question

If h = 17 units and r = 9 units, then what is the volume of the cone?

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

Given:
- \( h = 17 \) units,
- \( r = 9 \) units,

We can substitute these values into the formula:

\[
V = \frac{1}{3} \pi (9)^2 (17)
\]

Calculating \( 9^2 \):

\[
9^2 = 81
\]

Now substitute this value back into the volume formula:

\[
V = \frac{1}{3} \pi (81)(17)
\]

Next, calculate \( 81 \times 17 \):

\[
81 \times 17 = 1377
\]

Putting that back in:

\[
V = \frac{1}{3} \pi (1377)
\]

Now, calculate \( \frac{1377}{3} \):

\[
\frac{1377}{3} = 459
\]

Thus, the volume is:

\[
V = 459\pi
\]

If you want a numerical approximation using \( \pi \approx 3.14 \):

\[
V \approx 459 \times 3.14 \approx 1446.06
\]

Therefore, the volume of the cone is:

\[
\boxed{459\pi} \text{ cubic units} \quad \text{or approximately } 1446.06 \text{ cubic units}.
\]