Problem 6. The radius of the base of a right circular cylinder is 6, and its height is 8. On the circle bounding the upper base, points $X$ and $Y$ are marked such that one of the arcs with endpoints at points $X$ and $Y$ equals $120^{\circ}$. Find the area of the section of the cylinder by a plane passing through points $X, Y$, and the center of the cylinder. If necessary, round the answer to 0.01.
Answer: $20 \pi+30 \sqrt{3} \approx 114.79$.