Question

A wire when bent in the form of a square encloses an area of 484cm². If the same wire is bent into the form of a circle, find the area of the circle.

Answer 1

The side of a square whose area is 484cm²
= `sqrt(484)`
= 22cm
⇒ The perimeter of the square = 4 x 22cm
The Circumference of a Circle with radius r = 2πr
Here, 
2πr = 4 x 22cm

⇒ r = `(88)/(2pi)`

= `(88 xx 7)/(2 xx 22)`
= 14cm
The Area of a Circle with radius r = πr²
The Area of a Circle with radius 14 = π(14)²

= `(22)/(7) xx (14)^2`
= 22 x 2 x 14
= 616cm².