When a wire is bent in the form of a square it encloses an area of 484sqcm what will be the area of the figure formed when the same wire is bent to form a circle?

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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.

Area of the circle = 484 cm2
Area of the square = Side2 

⇒ 484 = Side2 

⇒ 222 = Side2

⇒ Side = 22 cm

Perimeter of the square = 4 × Side

Perimeter of the square = 4 × 22

                                       = 88 cm

Length of the wire = 88 cmCircumference of the circle = Length of the wire = 88 cmNow, let the radius of the circle be r cm.

​Thus, we have:

2πr = 88

`⇒ 2xx22/7xx"r"=88`

⇒ r = 14

Area of the circle = πr2 

`=22/7xx14xx14` 

= 616 cm2 

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

Concept: Circumference of a Circle

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