The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is

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KollegeApply · Accepted Answer

$\frac{1}{14}$ Let x be the radius of the circle and y be its circumference. x = 28 cm ∆ x = 0 . 01 cm x = 2$\pi$ r y = $\pi$ r^2 = $\pi$ $\times$ x^$\frac{2}{4}$ $\pi$^2 = x^$\frac{2}{4}$$\pi$ \Rightarrow dy/dx = x/2$\pi$ \Rightarrow ∆ y/y = x/2$\pi$ ydx = 2/x $\times$ 0 . 01 \Rightarrow ∆ y/y $\times$ 100 = 2/x = $\frac{1}{14}$ \text { Hence, the percentage error in the area is } $\frac{1}{14}$ .

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