Multiple choice

The error in the measurement of radius of sphere is $0.3$%, what is percentage error in the measurement of its volume?

  1. $0.3$%
  2. $0.6$%
  3. $0.9$%
  4. $\dfrac { 4 }{ 3 } \pi { \left( 0.3 \right) }^{ 3 }$
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C Correct answer
Explanation

Volume of a sphere V = (4/3) * pi * r^3. The relative error in volume is 3 times the relative error in radius. Given the error in radius is 0.3%, the error in volume is 3 * 0.3% = 0.9%.

AI explanation

The volume of a sphere is proportional to the cube of its radius. Because the radius has an error of 0.3%, the percentage error in the volume is three times this value. Multiplying 0.3 by 3 gives an error of 0.9%.

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