1. **State the problem:** Calculate the volume of a cone-shaped megaphone with height $h=8$ inches and radius $r=9$ inches.
2. **Formula for volume of a cone:**
$$V=\frac{1}{3}\pi r^2 h$$
where $r$ is radius and $h$ is height.
3. **Substitute values:**
$$V=\frac{1}{3}\pi (9)^2 (8)$$
4. **Calculate $9^2$:**
$$9^2=81$$
5. **Plug in:**
$$V=\frac{1}{3}\pi \times 81 \times 8$$
6. **Multiply 81 and 8:**
$$81 \times 8=648$$
7. **Simplify fraction:**
$$V=\frac{1}{3}\pi \times 648=\pi \times \cancel{\frac{1}{3} \times 648}=\pi \times 216$$
8. **Calculate volume:**
$$V=216\pi \approx 678.58$$
9. **Round to nearest tenth:**
$$678.6 \text{ cubic inches}$$
**Final answer:** The volume is approximately $678.6$ cubic inches.
Cone Volume Bc0862
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.