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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.
Solution
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
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