Question

a circle of maximum possible size is cut from a square sheet of board .subsequently a square maximum possible size can be cut from the resultant circle what will be the area of the final square

Answer 1

Let a be the side of a square sheet .
                                                        2
Then,area of big square sheet=a  
Now , we make circle of maximum possible size from it .
Then the radius of a circle = a/2
So,its diameter(d)=2 x a/2 = a
Now,any square in a circle of maximum size will have the length of diagonal equal to the diameter of the circle .
i.e.diagonal of square made inside the circle = a
so the side of this square =a/square root of 2
                                                       2
Therefore,Area of this square=a  /2
area of final square is 1/2 of original square .

Answer 2

Answer:

From the figure :

Area of final square PQRS is half the area of the square ABCD