KöMaL 2024 K821

A cylindrical, open-top container was placed inside a cubic, open-top container with a side length of 1 meter, and it was fixed to the bottom of the cubic container. Water flows uniformly from a tap into the cubic container. We observe that the water level on the wall of the cube rises steadily for 10 minutes, then stops rising for 10 minutes, and then when it starts to rise again, it takes another 20 minutes for the cubic container to fill completely. Find the radius of the base and the height of the cylindrical container.