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Question
A steel wire, when bent in the form of a square, encloses an area of 121 cm2. The same wire is bent in the form of a circle. Find area the circle.
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Solution
Area of a square = ( Side )2
⇒ 121 = ( Side )2
⇒ Side of a square = 11 cm
Now,
The perimeter of a square = Perimeter of a circle
⇒ 4 x Side = Perimeter of a circle
⇒ 4 x 11 = Perimeter of a circle
⇒ Perimeter of a circle = 44 cm
⇒ 2πr = 44 ....( r is radius of a circle )
⇒ r = `44/[2π] = 44/[ 2 xx 22/7]` = 7 cm
∴ Area of a circle = πr2 = `22/7 xx 7 xx 7 = 154 "cm"^2`
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