2. A cube with edge $a=1 / \sqrt{2}$ is illuminated by a cylindrical beam of light with radius $\rho=\sqrt{2-\sqrt{3}}$, directed along the main diagonal of the cube (the axis of the beam contains the main diagonal). Find the area of the illuminated part of the cube's surface.
Answer: $\left(\sqrt{3}-\frac{3}{2}\right)(\pi+3)$.