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.
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
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?
A triangle, a square, a pentagon, a hexagon, an octagon and a circle all have an equal perimeter, which one has the smallest area?
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.
If the area of the larger square is subtracted from twice the area of the smaller square, then the result is 8 cm^2. However, if 3 times the area of the smaller square is added to 2 times the area of the larger square, then the result is 236 cm^2. Determine the side of the two squares.
