Question 3A circle of maximum possible size is cut from

SOLUTION

Let a be the side of a square sheet.

Then, area of bigger square sheet $=a^2$               ...(i)
Now, we make the circle of maximum possible size from it.     
Then, the radius of circle $\frac{a}{2}$                       ...(ii)
So, its diameter (d) $=2.\frac{a}{2}=a$
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 $=\frac{a}{\sqrt{2}}$                $[\because diagonal=side\sqrt{2}]$
$\therefore$ Area of this square $=\frac{a^2}{2}$                     ...(iii)
From Eqs. (i) and (iii),
Area of final square is $\frac{1}{2}$ of original square.