Percentage uncertainty in volume sums relative uncertainties of dimensions

Steps:

• Calculate percentage uncertainty for each side: (0.1 mm / side length) × 100%.
• For 20 mm: (0.1/20) × 100% = 0.5%.
• For 40 mm: (0.1/40) × 100% = 0.25%.
• For 10 mm: (0.1/10) × 100% = 1%. Total: 0.5% + 0.25% + 1% = 1.75% ≈ 1.8%.

Why B is correct:

• For volume V = l × w × h, maximum percentage uncertainty is sum of individual percentage uncertainties, per error propagation rules for products.

Why the others are wrong:

• A: Underestimates by ignoring sum; treats as single uncertainty.
• C: Averages uncertainties instead of summing relatives.
• D: Misapplies absolute uncertainty to volume directly.

Final answer: B