Uncertainty propagation for spherical density calculation Steps:

• Relative uncertainty in diameter Δd/d = 0.2 mm / 20 mm = 0.01 (1%), treating nominal d as 20 mm for consistent units and reasonable density.
• Volume V ∝ d³, so relative uncertainty in V = 3 × (Δd/d) = 3 × 0.01 = 0.03 (3%).
• Relative uncertainty in mass Δm/m = 0.05 / 2.06 ≈ 0.024 (2.4%), which is comparable but secondary.
• For ρ = m/V, percentage uncertainty ≈ sum of relatives = 2.4% + 3% = 5.4%; best estimate per options is dominant 3% from volume.

Why D is correct:

• For a sphere, V = (4/3)π(r)^3 with r = d/2, so δV/V = 3 δd/d by power rule for uncertainty propagation in calculated quantities.

Why the others are wrong:

• A. Underestimates by ignoring volume contribution or misapplying mass alone.
• B. Similar underestimation, perhaps halving the diameter relative error.
• C. Approximates mass uncertainty (0.05/2.06 ≈ 2.4%) but neglects volume term.

Final answer: D