Hello guys, new member here. I've got a calculus project due Tuesday that I could use some help on. I won't bore you with the all details of the project, but first let's imagine an olive in the shape of a perfect sphere (with a radius always bigger than 6mm) that goes through a set of blades 6mm apart. This chops congruent caps off each side of the olive. Then, a machine takes a punch and punches out the center of the olive. The diameter of the punch always matches the diameter of the circle left behind when the caps were lopped off by the blades. I need to verify if the diameter of the original olive will affect the volume of the final pitted olive. I was thinking I could set up a double or triple integral to find the volume of a sphere centered at the origin in between the planes z=-3 and z=3 with the bounds on my radius being the radius of the pitted portion and the overall radius of the olive. However, I'm not sure exactly how to set it up. Any ideas? If you're having trouble picturing this I've attached a sketch to help visualize the problem. Thanks in advance!!