A wire encloses an area of 616 cm² when it is bent in the form of a circle. If the wire is bent in the form of a square, then its area (in cm²) is very nearly equal to: (Take $π =\frac{22}{7}$)

484

Area of circle = 616 cm²

Area of a circle = πr² 

\(\frac{22}{7}\)×  r² = 616

= r² = 616 × \(\frac{7}{22}\)= 28 × 7

= r = \(\sqrt {2 × 2 × 7 × 7}\)

= r = 2 × 7 = 14 cm

Circumference of the circle  = 2 × \(\frac{22}{7}\) × 14 = 88cm

As we know, perimeter of the square = Circumference of the circle

= 4a = 88

= a = 22

Area of the square = a² = 22 × 22 = 484cm²