GATE 2022 CE (CE2) – Question 29
The error in measuring the radius of a 5 cm circular rod was 0.2%. If the cross-sectional area of the rod was calculated using this measurement, then the resulting absolute percentage error in the computed area is______. (round off to two decimal places)
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Correct answer: 0.39 to 0.41
Explanation
For $A=\pi r^2$, logarithmic differentiation gives $dA/A=2dr/r$. The area percentage error is therefore twice the radius percentage error.
Hence error = $2(0.2)=\mathbf{0.40\%}$. Using the exact increase gives 0.4004%, which rounds to the same value.