GATE 2022 CH – Question 28
The area of a circular field is 25 m$^2$. The radius, $r$, is to be determined using the Newton-Raphson iterative method. For an initial guess of $r = 2.500$ m, the revised estimate of $r$ after one iteration is ___________ m (rounded off to three decimal places).
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Correct answer: 2.828 to 2.856
Explanation
Let $f(r) = \pi r^2 - 25$ and $f'(r) = 2\pi r$. At $r = 2.5$: $f = 19.635 - 25 = -5.365$ and $f' = 15.708$. So $r_1 = 2.5 + \frac{5.365}{15.708} = 2.842$ m.