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Question
A metal wire, when bent in the form of a square of largest area, encloses an area of 484 cm2. Find the length of the wire. If the same wire is bent to the largest circle, find:
(i) radius of the circle formed.
(ii) area of the circle.
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Solution
Area of the square made wire = 484 cm2
∴ Length (side) = `sqrt"Area"=sqrt484` = 22 cm
(i) Perimeter of wire = 4 × Side
= 4 × 22 = 88 cm
∴ Circumference of circular wire = 88 cm
∴ Radius (r) = `"C"/(2π)=(88xx7)/(2xx22)"cm"` = 14 cm
(ii) ∴ Area of the circle = πr2
= `22/7xx14xx14` = 616 cm2
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