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Question

A copper wire when bent in the form of a square encloses an area of 484 cm2. The same wire is not bent in the form of a circle. Find the area enclosed by the circle.

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Solution

Area of the circle = 484 cm2
Area of the square = Side2
484=Side2222=Side2Side=22 cm
Perimeter of the square = 4×Side
Perimeter of the square = 4×22
= 88 cm
Length of the wire = 88 cm
Circumference of the circle = Length of the wire = 88 cm
Now, let the radius of the circle be r cm.
​Thus, we have:
2πr=882×227×r=88r=14

Area of the circle = πr2
=227×14×14=616 cm2

Thus, the area enclosed by the circle is 616 cm2.

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