Volume from spring constant and Young's modulus Steps:

• Young's modulus relates to spring constant via k = Y A / L, where A is cross-sectional area.
• Rearrange for A: A = k L / Y.
• Volume V = A L = k L² / Y.
• Substitute k = 2.7 × 10^{-1} N/m, L = 2.4 m, Y = 1.3 × 10^{10} Pa: V = (0.27 × 5.76) / 1.3 × 10^{10} = 1.2 × 10^{-6} m³. Why D is correct:
• The formula V = k L² / Y directly from k = Y A / L and V = A L yields 1.2 × 10^{-6} m³, matching the derived volume. Why the others are wrong:
• A overestimates by factor of ~2, likely from doubling L² miscalculation.
• B underestimates by half, possibly from halving k erroneously.
• C overestimates by ~4, perhaps from using L instead of L².

Final answer: D