A square ABCD is inscribed in a circle of unit radius. Semicircles are described on each side of a diameter. The area of the region bounded by the four semicircles and the circle is

Radius of the circle = 1 unit, => Diameter = BD = 2 units

Thus, side of square = AB = $$\sqrt2$$ units

Radius of a semi-circle = $$\frac{AB}{2}=\frac{\sqrt2}{2}=\frac{1}{\sqrt2}$$

=> Area of 4 semi-circles = $$2\pi r^2$$

= $$2\pi (\frac{1}{\sqrt2})^2=\pi$$ sq. units ------------(i)

Area bounded by region = Area of circle - Area of square

= $$\pi(1)^2-(\sqrt2)^2=(\pi-2)$$ sq. units ---------------(ii)

$$\therefore$$ Required area bounded by 4 semi circles = (i) - (ii)

= $$\pi - (\pi-2) = 2$$ sq. units

=> Ans - (B)