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

• A. 6
• B. 12
• C. 16
• D. 4

Hint:

For scaling errors: length → area → volume: multiply linear relative error by powers 1,2,3 respectively.

Answer 1

The Correct Option is B

• 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).