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AP EAMCET202119 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

If the error committed in measuring the radius of the circle is 0.05 % , then the corresponding error in calculating the area is

Options

  1. A0 . 05 %
  2. B0 . 0025 %
  3. C0 . 25 %
  4. D0 . 1 %

Correct answer

D. 0 . 1 %

Step-by-step solution

Area of circle,   A = π r 2 Apply log on both sides ⇒     log ⁡ A = l o g π + 2 log ⁡ r Differentiating w.r.t. x ⇒   ∆ A A = 2 × ∆ r r   = 2 × 0.05   = 0.1 %

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