Let's break down the problem from your image: ### **Question** Calculate the percentage cold work for a specimen having strain value as .15 in/in. --- ### **Formula for Percentage Cold Work** Percentage Cold Work (%CW) is calculated as\[ \% \text{ Work} = \left( \frac{\text{Initial Area} - \text{Final Area}}{\text{Initial Area}} \right) \times 100 \] But, when strain (true strain, ε) is given, the relationship is: \[ \text{True Strain} (\epsilon) = \ln \left( \frac{A_}{A_f} \right) \] Where, - \( A_ \) = Initial Area - \( A_f \) = Final Area So, \[ \frac{A_}{A_f} = e^{\epsilon} \] \[ A_f = \frac{A_}{e^{\epsilon}} \] So, \[ \% \text{Cold Work} = \left[ 1 - \frac{A_f}{A_} \right] \times 100 \] \[ \% \text{Cold Work} = \left[ 1 - \frac{1}{e^{\epsilon}} \right] \times 100 \] --- ### **Calculation** Given: \(\epsilon = .15\) in/in \[ e^{.15} \approx 1.1618 \] \[ \frac{1}{e^{.15}} \approx .8607 \] \[ \% \text{Cold Work} = (1 - .8607) \times 100 \approx 13.04\% \] --- ### **Correct Option** **13.04%** This matches the last option in your list. --- ## **Summary Table** | Option | Value | |----------------|-----------| | (a) | 15.06% | | (b) | 17.09% | | (c) | 10.89% | | (d) | 13.04% | **← Correct** | --- **Select: 13.04%**