Subjects geometry

Megaphone Volume Cbdba4

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1. **State the problem:** We need to find the volume of a megaphone shaped like a cone with a height of 8 inches and a base radius of 9 inches. 2. **Formula for the volume of a cone:** $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Substitute the given values:** $$V = \frac{1}{3} \pi (9)^2 (8)$$ 4. **Calculate the squared radius:** $$9^2 = 81$$ 5. **Plug in the squared radius:** $$V = \frac{1}{3} \pi \times 81 \times 8$$ 6. **Multiply 81 and 8:** $$81 \times 8 = 648$$ 7. **Simplify the fraction:** $$V = \frac{1}{3} \pi \times 648 = \pi \times \cancel{\frac{1}{3} \times 648} = \pi \times 216$$ 8. **Calculate the volume:** $$V = 216 \pi \approx 216 \times 3.1416 = 678.58$$ 9. **Round to the nearest tenth:** $$678.6 \text{ cubic inches}$$ **Final answer:** The volume of the megaphone is approximately $678.6$ cubic inches.