Question

A wire is in the form of a circle of radius 42 cm. It is bent into a square.
Determine the side of the square and compare the area of the regions enclosed in two cases. 

Answer 1

Radius of the circle= 42 cm 

Area of the cirde = π r² 

`= 22/7 xx 42 xx 42`

= 5544 cm²

Area of the cirde = 5544 cm²

Circumference of the circle = 2 π r

`= 2 xx 22/7 xx 42`

= 264 cm

Perimeter of the square = Circumference of the circle = 264 cm 

4 x side = 264 

side = `264/4` = 66 cm

Side of square =66 cm 

Area of square = side² = 66 x 66 = 4356 cm² 

Area of a circle : Area of square = `5544/4356 = 14/11`

Side of square = 66 cm

Area of the cirde: Area of square = 14 : 11