A student has two open-topped containers: the larger one is a right circular cylinder of height 21 cm and radius 12 cm, the smaller one is a right circular cone of height 20 cm and radius 10 cm (at the open end). (The walls of the two containers are thin enough so that their widths can be ignored.) The larger container initially has water in it to a depth of 18 cm. The student slowly lowers the cone into the larger container, keeping the top (open side) of the cone horizontal. As the cone is lowered, water may first overflow out of the larger container, but eventually water pours into the cone. When the tip of the cone is resting on the bottom of the cylinder, what is the depth of the water in the cone?