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JEE Main20266 April 2026Evening ShiftPhysicsUnits and DimensionsActual

The percentage error in the calculated volume of a sphere, if there is 2 % error in its diameter measurement, is __________.

Options

  1. A1
  2. B2
  3. C6
  4. D8

Correct answer

C. 6

Step-by-step solution

The volume of a sphere in terms of its diameter D is given by V = 6 D^3 Taking the natural logarithm on both sides, we get V = ( 6 ) + 3 D Differentiating for small errors, we obtain V V = 3 D D Multiplying by 100 to find the percentage error, V V 100 = 3 ( D D 100 ) Given that the percentage error in the diameter is 2 % , we have D D 100 = 2 Therefore, the percentage error in the volume is 3 2 = 6 % Answer: 6

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