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MHT CET202521 Apr 2025Evening ShiftPhysicsMathematics in PhysicsActual

Error in the measurement of radius of the sphere is 2 % . The error in the calculated value of its volume is

Options

  1. A3 %
  2. B2 %
  3. C6 %
  4. D9 %

Correct answer

C. 6 %

Step-by-step solution

The volume of a sphere is given by V = 4 3 r^3 , where r is the radius. Since V is proportional to r^3 , the percentage error in volume relates to the percentage error in radius by the power rule: V V 100 % = 3 ( r r 100 % ) Given that the radius has a 2 % error, the volume error becomes: V V 100 % = 3 2 % = 6 % Answer: C

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