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A copper wire when bent in the form of a hexagon encloses an area of 726*Sqrt(3) cm^2....

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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.

posted Nov 24, 2015 by anonymous

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1 Answer

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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

answer Nov 24, 2015 by Jaikumar Bhatia



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