Question Detail
Question
If the uncertainty in measuring the radius of a sphere is 2%, what is the approximate percentage uncertainty in its volume?
Correct Answer
Option C is the correct answer.
Detailed Explanation
The volume V of a sphere is given by V = (4/3)πr³. According to the power rule for uncertainties, the percentage uncertainty in V is 3 times the percentage uncertainty in r. Therefore, %ΔV = 3 × 2% = 6%.
Hint
When a quantity is raised to a power, the percentage uncertainty is multiplied by that power. Volume depends on the cube of the radius.