A wire bent in the form of a circle of radius 42 cm is cut and again bent in the form of a square. Find the ratio of the areas of the regions enclosed by the circle and the square.
Given,
Radius of circle made by wire, r = 42 cm
Circumference of circle of radius r = 2πr
Circumference of circle made by wire
As, the same wire is bent to make a square the perimeter of square will be equal to circumference of circle.
Let the side of square be a.
Perimeter of square of side 'a' = 4a
We have,
4a = 264
a = 66 cm
Now,
Ratio of areas
Area of circle of radius r = πr2
Area of square of radius a = a2
Putting value, we get
Ratio of areas
Required ratio is 14 : 11
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