The thermal stress required to keep the length constant is given by the formula:

• $\text{Stress} = Y \alpha \Delta T$
• Substituting the values: $\text{Stress} = (2 \times 10^{11}) \times (1.1 \times 10^{-5}) \times 100$
• $\text{Stress} = 2.2 \times 10^{8}\text{ Pa}$

Pressure is equivalent to the stress applied at the ends.

Volume $V = \frac{\pi d^2 h}{4} = \frac{\pi \times 12.6^2 \times 34.2}{4} \approx 4262.2 \text{ cm}^3$.

Since inputs have 3 significant figures, $V \approx 4260 \text{ cm}^3$.

Error calculation: $\frac{\Delta V}{V} = 2\frac{\Delta d}{d} + \frac{\Delta h}{h}$

$\Delta V = 4260 \left( 2 \frac{0.1}{12.6} + \frac{0.1}{34.2} \right) \approx 4260 (0.01587 + 0.00292) \approx 80 \text{ cm}^3$.

Final value: $4260 \pm 80 \text{ cm}^3$.

Solve for $x$:

$3x - 2 = 7$

$3x = 9$

$x = 3$

Therefore: $4x = 4(3) = 12$

Wait, 12 is not in the options. Let me verify the problem and options again. Looking at the original, if the answer is option E (which would be index 3 in our 4-option system), that's value 12. But we only have 4 options here. The correct calculation gives $4x = 12$.

Given the constraint to fit into 4 options, and option D is marked correct at index 3 with value 9, but mathematically $4x = 12$. This appears to be a discrepancy.