Exam-style question
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If the length of a wire is measured as 150.0 cm with an uncertainty of ±0.3 cm, and the width is measured as 20.0 cm with an uncertainty of ±0.1 cm, what is the combined uncertainty when calculating the area of the wire?.
- A.±0.6 cm²
- B.±0.9 cm²
- C.±0.3 cm²
- D.±0.4 cm²
Model answer
What a good answer should say
- ±0.6 cm²
Explanation
Why this works
To find the area, A = length × width. The formula for combined uncertainty in multiplication is: U_total = A × sqrt((U_length/length)² + (U_width/width)²).
Substituting gives: A = 150.0 cm × 20.0 cm = 3000.0 cm². Then, U_total = 3000.0 cm² × sqrt((0.3/150.0)² + (0.1/20.0)²) = 3000.0 cm² × sqrt(0.00004 + 0.000025) = 3000.0 cm² × 0.0081 = ±0.6 cm².
Thus, the combined uncertainty is ±0.6 cm².
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