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If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of the volume of the sphere will be

Asked in CBSE AIPMT 2008 · Error in a power

Answer: (4) 6%

Step-by-step solution

Given: (Δ r)/r×100=2%.

V=4/3π r³

Idea: the exponent multiplies the fractional error; it is not an exponent on the error.

(Δ V)/V=3(Δ r)/r

(Δ V)/V×100=3×2=6%

Why the other options are wrong

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