Question

Find the volume, in cubic inches, of a cone with a radius of 17 inches, and a height of 32 inches. Round your answer to the nearest hundredth. use 3.14 for pi.
- 1708.16
- 29038.72
- 7259.68
- 4624
- 9679.57
- 427.04

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

Here, the radius \( r = 17 \) inches and the height \( h = 32 \) inches. Using \( \pi \approx 3.14 \), we can calculate the volume:

1. Calculate the base area \( r^2 \):
\[
r^2 = 17^2 = 289
\]

2. Now, plug the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 289 \times 32
\]

3. Start by calculating \( 3.14 \times 289 \):
\[
3.14 \times 289 \approx 907.46
\]

4. Now multiply that by 32:
\[
907.46 \times 32 \approx 29038.72
\]

5. Finally, divide by 3 to get the volume:
\[
V \approx \frac{29038.72}{3} \approx 9680.24
\]

Rounding to the nearest hundredth, we find:

\[
V \approx 9680.24
\]

Among the options given, the closest one is:

- **9679.57** (as it's likely meant to represent an approximation).

Thus, the volume of the cone is approximately **9679.57 cubic inches**.