A copper wire when bent in the form of a hexagon encloses an area of 726*Sqrt(3) cm^2. If the wire is bent to form a circle, find the area enclosed by it.

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A copper wire when bent in the form of a hexagon encloses an area of 726*Sqrt(3) cm^2. If the wire is bent to form a circle, find the area enclosed by it.

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Area of Hexagon=[3*Sqrt(3)/2]*a^2.................................(a=side of Hexagon)

726*Sqrt(3)=[3*Sqrt(3)/2]*a^2..............................................(i)

Simplify (i)

a=Sqrt(484)

Perimeter of Hexagon=6*a=6*Sqrt(484)..........................(ii)

Perimeter of circle=Pi*d=Perimeter of Hexagon............(iii)

Pi*d=6*Sqrt(484)...................................................from (ii)&(iii)

d=(6/Pi)*Sqrt(484).................................................................(iv)

Area of Circle=(Pi/4)*d^2

=1386..............................[by putting the value of 'd' from (iv)]

Ans is 1386Cm^2

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