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**.
Hollow Pipe Volume 9D1E6C
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