If the percentage error in the radius of circle is 3 , then the percentage error in its area is

If the percentage error in the radius of circle is 3 , then the percentage error in its area is
  1. 6
  2. $\frac{3}{2}$
  3. 2
  4. 4

Solution

$\begin{aligned} & \text { Given } \frac{d r}{r}=\frac{3}{100} \\ & A=\pi r^2 \Rightarrow d A=2 \pi r d r \\ & \Rightarrow \frac{d A}{A}=\frac{2 \pi r d r}{\pi r^2}=\frac{2 d r}{r}=\frac{6}{100} \Rightarrow \frac{d A}{A} \times 100=6 \%\end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 2)

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