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

333 views

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

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

Similar Puzzles

If a piece of wire 40 cm long is bent into a arc of a circle subtending an angle of 60 degree at the center, then what is the radius of the circle?

+1 vote

A triangle, a square, a pentagon, a hexagon, an octagon and a circle all have an equal perimeter, which one has the smallest area?

+1 vote

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal parts. Find the total length of the silver wire required.