Question

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 -

• A. 4225 m²
• B. 2050 m²
• C. 3025 m²
• D. 2650 m²
• E. 2750 m²

Answer 1

The correct option is C

3025 m²

Perimeter of square = Perimeter of circle

$4a=2\pi r$

$\begin{array}{c}\Rightarrow \frac{a}{r}=\frac{\pi }{2}\Rightarrow \frac{Areaofsquare}{Areaofcircle}=\frac{a^2}{\pi r^2}=\frac{1}{\pi }{\left(\frac{a}{r}\right)}^2\\ =\frac{1}{\pi }{\left(\frac{\pi }{2}\right)}^2=\frac{\pi }{4}\\ \Rightarrow \text{Area of square}=\frac{\pi }{4}\left(\text{area of circle}\right)=\frac{\pi }{4}\times 3850=3025m^2\end{array}$