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

If the error committed in measuring the radius of the circle is 0.05%, then the corresponding error in calculating the area is
  1. 0.05%
  2. 0.0025%
  3. 0.25%
  4. 0.1%

Solution

Area of circle,  A=πr2

Apply log on both sides

⇒  log⁡A=logπ+2log⁡r

Differentiating w.r.t. x

⇒ ∆AA=2×∆rr

 =2×0.05

 =0.1%

Asked in: AP EAMCET 2021 (19 Aug Shift 1)

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