Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height , as shown in the figure. It turns out that each ring will have exactly the same amount of wood as the other!
Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius through the center of a sphere of radius (with ). Express your final answer only in terms of .