Resistivity from resistance formula for uniform cylinder

Steps:

• Convert units to meters: length L = 80 mm = 0.08 m, diameter = 20 mm = 0.02 m, radius r = 0.01 m.
• Compute cross-sectional area A = π r² ≈ 3.14 × (0.01)² = 3.14 × 10^{-4} m².
• Apply formula ρ = R A / L, where R = 20 Ω.
• Substitute values: ρ = 20 × (3.14 × 10^{-4}) / 0.08 ≈ 0.0785 Ωm, which rounds to 0.10 Ωm.

Why B is correct:

• Matches the calculated value using ρ = R A / L, the definition of resistivity for a conductor.

Why the others are wrong:

• A. 0.03 Ωm underestimates by omitting π from area (A ≈ 10^{-4} m² gives 0.025 Ωm).
• C. 0.42 Ωm overestimates by using diameter as radius (A ≈ 1.26 × 10^{-3} m² gives 0.31 Ωm).
• D. 5 Ωm greatly overestimates, likely from unit conversion errors like treating mm as cm.

Final answer: B