A wire, when bent in the form of a square, encloses an area of $484 c m^{2}$ . Find area when the same wire is bent to form a circle.

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Solution

Area of square wire $= {s i d e}^{2} = 484 {c m}^{2}$
Hence, length of side $= \sqrt{484} = 22 c m$
Length of the wire $=$ Perimeter of the square $= 4 \times 22 = 88 c m$
The same $88 c m$ wire is used to make a circle.
Hence, circumference of the circle $= 88 c m$
$=> 2 π \times r a d i u s = 88 c m$
$=> 2 \times \frac{22}{7} \times r a d i u s = 88 c m$
Radius of the circle formed $= 14 c m$
Area of a circleformed $A = π r^{2}$
Area of the circle formed $= \frac{22}{7} \times 14 \times 14 = 616 {c m}^{2}$

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