Assume that if the shear stress in steel exceeds about `4.00xx10^(8)N//m^(2)` the steel ruptures. Determine the shearing force necessary to `(a)` shear a steel bolt `1.00 cm` in diameter and `(b)` punch a `1.00 cm` diameter hole in a steel plate `0.500 cm` thick.

Explanation

To solve the problem of determining the shearing force necessary to shear a steel bolt and punch a hole in a steel plate, we will follow these steps:

### Given Data:
- Shear stress limit for steel, \( \sigma = 4.00 \times 10^8 \, \text{N/m}^2 \)
- Diameter of the bolt and hole, \( d = 1.00 \, \text{cm} = 1.00 \times 10^{-2} \, \text{m} \)
- Thickness of the plate, \( t = 0.500 \, \text{cm} = 0.500 \times 10^{-2} \, \text{m} \)

### (a) Shearing Force to Shear a Steel Bolt
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