A circle of maximum possible is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of final square?

Question

Philoid · Accepted Answer

Let a be the side of a square sheet

Then area of bigger square sheet = a² …..1

Now, we make the circle of maximum possible size from it.

Then the radius of circle = ………….2

So its diameter = a

Now, any square in a circle of maximum size will have the length of diagonal equal to the diameter of circle.

i.e. diagonal of square made inside the circle = a

so, the side of this square =

Area of this square =

From eqs.1and 2,

Area of final square is of original square.