Multiple choice

If the error in the volume of a sphere is 9%, what is the error in measurement of its radius ?

  1. 1%

  2. 9%

  3. 3%

  4. 6%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume V = (4/3) * pi * r^3. Taking logarithmic differentiation, dV/V = 3 * dr/r. If dV/V = 9%, then 3 * dr/r = 9%, so dr/r = 3%.

AI explanation

The volume of a sphere is calculated using the formula V = (4/3) * pi * r^3, meaning volume is proportional to the cube of the radius. If the error in volume is 9 percent, the error in the radius is found by taking the cube root of the volume error. The cube root of 1.09 is approximately 1.029, which indicates the radius error is approximately 3 percent.

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