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Question
A wire when bent in the form of a square encloses an area of 484cm2. If the same wire is bent into the form of a circle, find the area of the circle.
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Solution
The side of a square whose area is 484cm2
= `sqrt(484)`
= 22cm
⇒ The perimeter of the square = 4 x 22cm
The Circumference of a Circle with radius r = 2πr
Here,
2πr = 4 x 22cm
⇒ r = `(88)/(2pi)`
= `(88 xx 7)/(2 xx 22)`
= 14cm
The Area of a Circle with radius r = πr2
The Area of a Circle with radius 14 = π(14)2
= `(22)/(7) xx (14)^2`
= 22 x 2 x 14
= 616cm2.
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