Q. 254.6( 9 Votes )

Sumit cut a wire into two equal parts. One part he bent in the form of square and other part bent in the form of circle. If the area of circle exceeds that of the square by 33 sq. cm. Let us write by calculating the original length of the wire.

Answer :

It is given that the wire was cut into two equal parts which means perimeter of square and circle will be equal.


Perimeter of a square = 4× side


Circumference of a circle = 2π r


Let s be the side of the square and r be the radius of the circle.


According to the question,


4s = 2π r


2s = π r



..(1)


Also, it is given that the area of circle exceeds that of the square by 33 sq. cm.


Area of a circle = πr2


Area of a square = side× side


πr2= s2 + 33


From (1),







r = 7 cm


Circumference of a circle = 2π r



the wire was cut into two equal parts which means perimeter of square and circle will be equal.


Total length of wire = 44 + 44 = 88 cm


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