A rectangular parallelepiped has edges meeting at a vertex in the ratio $1: 2: 3$. How do the lateral surface areas of the right circular cylinders circumscribed around the parallelepiped compare?
$$
P_{1}: P_{2}: P_{3}=\sqrt{13}: 2 \sqrt{10}: 3 \sqrt{5}
$$

The problem was solved by: Andráschek F., Barabás S., Czank K., Deutsch N., Freibauer E., Kerekes T., Kohn B., Krisztián Gy., Lukhaub Gy., Obláth R., Oltay K., Spitzer Ö., Weisz J.