Multiple choice

If the percentage error in the measurement of the radius of the sphere is 4%, then the percentage error in the measurement of the volume is

  1. 4%

  2. 6%

  3. 12%

  4. 16%
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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 * (relative error in radius). 3 * 4% = 12%.

AI explanation

The volume of a sphere is proportional to the cube of its radius, meaning any percentage error in the radius is tripled for the volume. Therefore, a 4 percent error in the radius results in a 3 * 4 = 12 percent error in the volume.

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