The uncertainty recorded in the radius of a sphere is 1.6%. The uncertainty in the area of that sphere is:
Correct answer: B. 3.2%
- A. 4.8%
- B. 3.2%
- C. 1.6%
- D. 0.8%
Explanation
The uncertainty in a measurement involving exponentiation is multiplied by the exponent. For a sphere's area, which is proportional to the square of the radius, the formula for area is A = 4πr2. Therefore, the percentage uncertainty in the area is twice the percentage uncertainty in the radius. Given a 1.6% uncertainty in the radius, the area will have a 2 × 1.6% = 3.2% uncertainty.The incorrect options arise from misunderstanding how uncertainties propagate: 4.8% is calculated as if the exponent was 3, 1.6% is the original uncertainty in the radius, and 0.8% is an incorrect division.
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About Errors and Significant Figures
Measurement errors include random and systematic effects, absolute, fractional and percentage uncertainty, and the precision shown by significant figures. Questions apply rounding rules and uncertainty propagation in addition, subtraction, multiplication and division, while distinguishing accuracy from precision and uncertainty from an actual mistake.
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