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Question 3

A circle of maximum possible size 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 the final square?
(a) 34 of original square                  (b) 12 of original square
(c) 14 of original square                   (d) 23 of original square


Solution

Let a be the side of a square sheet.

Then, area of bigger square sheet =a2               ...(i)
Now, we make the circle of maximum possible size from it.     
Then, the radius of circle a2                       ...(ii)
So, its diameter (d) =2.a2=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 cirlce = a
So, the side of this square =a2                [diagonal=side2]
Area of this square =a22                     ...(iii)
From Eqs. (i) and (iii),
Area of final square is 12 of original square.

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