Uncertainty propagation for volume of a cube

Steps:

• Volume formula: V = s³, where s = 30.0 mm.
• Relative uncertainty in s: (0.1 / 30.0) × 100% = 0.333%.
• For V = s³, relative uncertainty in V is 3 × relative uncertainty in s = 3 × 0.333% = 1%.
• Percentage uncertainty in volume is 1%.

Why C is correct:

• Relative uncertainty for V = s^n follows δV/V = n × (δs/s); here n=3, so 3 × (0.1/30) × 100% = 1%.

Why the others are wrong:

• A: Equals side's percentage uncertainty, ignoring multiplication by 3.
• B: Approximates side's percentage uncertainty (0.333% ≈ 0.3%) but omits factor of 3.
• D: Overestimates by using absolute uncertainty (0.1 mm) directly or misapplying the factor.

Final answer: C