Multiple choice

In measuring the circumference $100$cm of a circle, there is an error of $0.05$cm then percentage error in its area is?

  1. $\dfrac{1}{10}$
  2. $\dfrac{1}{5}$
  3. $\dfrac{1}{100}$
  4. $1$
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A Correct answer
Explanation

C = 2*pi*r, so r = C/(2*pi). Area A = pi*r^2 = pi * (C/(2*pi))^2 = C^2 / (4*pi). dA/dC = 2C / (4*pi) = C / (2*pi). Error in A = (dA/dC) * error in C = (100 / (2*pi)) * 0.05 = 5 / (2*pi). Percentage error = (Error in A / A) * 100 = (5/(2*pi) / (100^2/(4*pi))) * 100 = (5/(2*pi) * 4*pi / 10000) * 100 = (10 / 10000) * 100 = 0.1 = 1/10.

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