Question

Find the volume of a cone with a height of 9 inches and a diameter of 12 inches. calculate the volume of the cone

Answer 1

To find the volume of a cone, you can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height.

1. **Find the radius**: The diameter of the cone is given as 12 inches. Therefore, the radius \( r \) is half of the diameter:

\[
r = \frac{diameter}{2} = \frac{12}{2} = 6 \text{ inches}
\]

2. **Use the height**: The height \( h \) of the cone is given as 9 inches.

3. **Plug the values into the volume formula**:

\[
V = \frac{1}{3} \pi (6)^2 (9)
\]

4. **Calculate \( r^2 \)**:

\[
(6)^2 = 36
\]

5. **Multiply by the height**:

\[
36 \times 9 = 324
\]

6. **Finally, calculate the volume**:

\[
V = \frac{1}{3} \pi \times 324 = \frac{324 \pi}{3} = 108 \pi
\]

7. **Using \(\pi \approx 3.14\)** for a numerical answer:

\[
V \approx 108 \times 3.14 \approx 339.12 \text{ cubic inches}
\]

Thus, the volume of the cone is approximately:

\[
\boxed{339.12} \text{ cubic inches}
\]

Or in terms of \(\pi\):

\[
\boxed{108\pi} \text{ cubic inches}
\]