TS EAMCET · Maths · Application of Derivatives
The circumference of a circle is measured as \(56 \mathrm{~cm}\) with an error \(0.02 \mathrm{~cm}\). The percentage error in its area is
- A \(1 / 7\)
- B \(1 / 28\)
- C \(1 / 14\)
- D \(1 / 56\)
Answer & Solution
Correct Answer
(C) \(1 / 14\)
Step-by-step Solution
Detailed explanation
Given circumference of a circle \(S=2 \pi r=56\) \(\begin{array}{ll}\Rightarrow & r=\frac{28}{\pi} \\ \text { Error } & \delta S=2 \pi \delta r=0.02 \\ \Rightarrow & \delta r=\frac{0.02}{2 \pi}\end{array}\) Area of circle, \(A=\pi r^2\) \(\therefore\) Percentage error in…
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