1. **State the problem:** Calculate the volume of iron in a hollow cylindrical pipe with outer diameter 11 in, thickness 0.45 in, and length 20 in. 2. **Formula used:** Volume of hollow cylinder is $$V = \pi h (R^2 - r^2)$$ where $h$ is length, $R$ outer radius, $r$ inner radius. 3. **Calculate radii:** - Outer radius $R = \frac{11}{2} = 5.5$ in - Thickness $t = 0.45$ in - Inner radius $r = R - t = 5.5 - 0.45 = 5.05$ in 4. **Calculate volume:** $$V = \pi \times 20 \times (5.5^2 - 5.05^2)$$ 5. **Simplify squares:** $$5.5^2 = 30.25$$ $$5.05^2 = 25.5025$$ 6. **Subtract inside parentheses:** $$30.25 - 25.5025 = 4.7475$$ 7. **Calculate volume:** $$V = \pi \times 20 \times 4.7475 = 20\pi \times 4.7475$$ 8. **Multiply constants:** $$20 \times 4.7475 = 94.95$$ 9. **Final volume:** $$V = 94.95 \pi \approx 94.95 \times 3.1416 = 298.29$$ 10. **Answer:** The volume of iron in the pipe is approximately **298.29 cubic inches**.