Use the resistance formula R = ρL/A to find wire length

Steps:

• Use R = ρL/A to rearrange for length: L = RA/ρ.
• Convert diameter to radius: r = 0.20 mm / 2 = 0.10 mm = 1.0 × 10^{-4} m.
• Calculate cross-sectional area: A = πr² = π(1.0 × 10^{-4})² = π × 10^{-8} m².
• Substitute values: L = (9.5 Ω)(π × 10^{-8} m²)/(4.0 × 10^{-7} Ω m) = 1.20 m.

Why A is correct:

• The formula R = ρL/A directly yields L = 1.20 m when substituting the given resistance, resistivity, and area.

Why the others are wrong:

• B: Results from using diameter instead of radius in area calculation, doubling A incorrectly.
• C: Arises from approximating π ≈ 3 and misplacing a decimal in the exponent.
• D: Comes from neglecting the factor of π in the area formula.

Final answer: A