A circular piece of metal of maximum area is cut out from a square piece and then a square piece of maximum area is cut out of the circular piece. What is the total area of wasted metal?

Dear Student ,
Please find below the solution to the asked query :

Let the side of a square be x units .

Area of square ABCD=x2 sq. units .A circular piece is cut out from square of side x units .From figure it is clear that Diameter of circle will be equal to the side of square .So, Radius of circle =x2 units .Now , Diagonal of square PQRS is equal to the diameter of circle as it can be seen from the figure .In PQR ,Applying Pythagoras theoremPQ2+QR2=PR2PQ2+PQ2=x2       Since PQRS is a square , So PQ=QR2PQ2=x2PQ=x2 units .Area of square PQRS=x22=x22 sq. units .Total area of wasted material = Area of square ABCD - Area of square PQRS=x2-x22=x22   Sq. units .

 
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