Analysis: The volume formula of cylinder is the bottom area multiplied by the height, and the volume formula of cone is 1/3 the bottom area multiplied by the height. It shows that the volume of a cone with the same base and height is only 1/3 of that of a cylinder with the same base and height.

Now we know that the bottoms of a cone and a cylinder are equal, and the volume ratio is 1: 6, which means that the height of a cylinder is twice that of a cone. So if the height of the cone is 4.2cm, the height of the cylinder is 4.2*2cm, and if the height of the cylinder is 4.2cm, the height of the cone is 4.2/2cm.