Subjects geometry

Hollow Pipe Volume 9D1E6C

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1. **State the problem:** We need to find the volume of the wall of a hollow steel pipe shaped like a right circular cylinder. 2. **Given data:** - Outside diameter $D = 60$ inches - Wall thickness $t = \frac{5}{8}$ inches - Height $h = 132$ inches 3. **Formula for volume of a hollow cylinder:** The volume of the wall is the difference between the volume of the outer cylinder and the inner cylinder. $$V = \pi h (R_{outer}^2 - R_{inner}^2)$$ where $R_{outer}$ is the outer radius and $R_{inner}$ is the inner radius. 4. **Calculate radii:** $$R_{outer} = \frac{D}{2} = \frac{60}{2} = 30$$ $$R_{inner} = R_{outer} - t = 30 - \frac{5}{8} = 30 - 0.625 = 29.375$$ 5. **Calculate the volume:** $$V = \pi \times 132 \times (30^2 - 29.375^2)$$ Calculate the squares: $$30^2 = 900$$ $$29.375^2 = 29.375 \times 29.375 = 862.890625$$ 6. **Subtract the squares:** $$900 - 862.890625 = 37.109375$$ 7. **Calculate the volume:** $$V = \pi \times 132 \times 37.109375$$ $$V = 3.1416 \times 132 \times 37.109375$$ $$V \approx 3.1416 \times 4899.65625$$ $$V \approx 15387.5$$ **Final answer:** The volume of the wall of the steel pipe is approximately **15387.5 cubic inches**.