4. A cube with edge $a=1$ is illuminated by a cylindrical beam of light with radius $\rho=\sqrt{2-\sqrt{2}}$, 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: $\frac{(2 \sqrt{3}-\sqrt{6})(\pi+6 \sqrt{2})}{4}$.

Lomonosov Moscow State University

## "Lomonosov" School Students Olympiad in Mathematics

Final Stage 2019/2020 academic year for 11th grade

## Problem 8