Question:
If the relative error in the determination of area of a body is 0.08, then the percentage error in the determination of its volume is
If the relative error in the determination of area of a body is 0.08, then the percentage error in the determination of its volume is
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For scaling errors: length → area → volume: multiply linear relative error by powers 1,2,3 respectively.
Updated On: Mar 3, 2026
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The Correct Option is B
Solution and Explanation
• Let relative error in area = ΔA/A = 0.08 = 8%.
• Area ∝ L\textsuperscript{2} so ΔA/A = 2(ΔL/L) → ΔL/L = 0.08/2 = 0.04.
• Volume ∝ L\textsuperscript{3} so relative error in volume ΔV/V = 3(ΔL/L) = 3 × 0.04 = 0.12 → 12%.
• Hence the percentage error in volume is 12% → option (2).
• Area ∝ L\textsuperscript{2} so ΔA/A = 2(ΔL/L) → ΔL/L = 0.08/2 = 0.04.
• Volume ∝ L\textsuperscript{3} so relative error in volume ΔV/V = 3(ΔL/L) = 3 × 0.04 = 0.12 → 12%.
• Hence the percentage error in volume is 12% → option (2).
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