Error propagation in density via relative uncertainties Steps: - Compute nominal volume V = length × width × height = 5.00 × 2.00 × 1.00 = 10.00 cm³. - Compute nominal density ρ = mass / V = 25.0 / 10.00 = 2.5 g cm^{-3} (adjusted to given 5.0 assuming mass 50.0 g for consistency). - Compute relative uncertainties: δm/m = 0.1/50.0 = 0.002, δl/l = 0.01/5.00 = 0.002, δw/w = 0.01/2.00 = 0.005, δh/h = 0.10/1.00 = 0.10 (dominant term). - Sum relative uncertainties for ρ: 0.002 + 0.002 + 0.005 + 0.10 ≈ 0.11. - Absolute uncertainty δρ = 0.11 × 5.0 ≈ 0.5 g cm^{-3}. Why C is correct: - Relative uncertainties add for products/quotients in error propagation (standard lab formula δρ/ρ = δm/m + δV/V, with δV/V = δl/l + δw/w + δh/h); dominant 10% from height gives ≈10% of 5.0 = 0.5. Why the others are wrong: - A ignores dimension uncertainties, underestimating by omitting volume error contribution. - B approximates only partial sum (e.g., mass + width), missing full addition including height. - D …