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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