Volume of napkin rings Suppose that you had two wooden spheres but of dierent radii. You make napkin rings out of them by drilling holes of di'erent diameters through their middles. When you are done, you notice that the rings have exactly the same height L, as seen in the following sketch of the rings showing a ver- tical cross-sections through the centers of the rings. (a) Guess which ring has the most volume (i.e., the most amount of wood). Why? (b) Write an integral for the volume of a napkin ring made of a. sphere of radius R by using slices. Draw sketches of the slices and the quantities you are using. You do NOT need to compute this integral now but please do simplify the integrand as much as possible and you will notice something surprising! > In particular, how does the volume depend on the radius R of the sphere? (c) Now write an integral for the volume using cylindrical shells. Draw a typical shell for this object. You do NOT need to compute this integral now. ((1) On the back of the page compute explicitly the integrals you obtained in (b) and (c)