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 $π =\frac{22}{7}$)
Answer & explanation
Correct answer: option 4
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