A cylindrical container has a radius of 3 centimeters and a height of 20 centimeters. It is completely filled with water. This water is then poured into a cube-shaped container and a cone-shaped container. The cube has an edge length of 10 centimeters, and the cone has a radius of 5 centimeters. How much water is in each container if the water is equally distributed between the cube and the cone? Express the final water level in the cone in terms of its height. Let's think step by step and output the final answer within \boxed{}.
user