The perimeter of a square and a circular field are same. If the area of the circular field is 3850 sq.m, then area of the square is -

4225

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3025

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2650

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2750

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Solution

The correct option is B
3025

$P e r i m e t e r o f s q u a r e = P e r i m e t e r o f c i r c l e$

$4 a = 2 π r$

$\begin{matrix} \Rightarrow \frac{a}{r} = \frac{π}{2} \Rightarrow \frac{A r e a o f s q u a r e}{A r e a o f c i r c l e} = \frac{a^{2}}{π r^{2}} = \frac{1}{π} {(\frac{a}{r})}^{2} = \frac{1}{π} {(\frac{π}{2})}^{2} = \frac{π}{4} \Rightarrow A r e a o f s q u a r e = \frac{π}{4} (a r e a o f c i r c l e) = \frac{π}{4} \times 3850 = 3025 m^{2} \end{matrix}$

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The perimeter of a square and a circular field are same. If the area of the circular field is 3850 sq.m, then area of the square is -

The correct option is B 3025 Perimeter of square = Perimeter of circle 4a=2πr ⇒ar=π2⇒Area of squareArea of circle=a2πr2=1π(ar)2=1π(π2)2=π4⇒Area of square =π4( area of circle)=π4×3850=3025 m2