Volume

This chapter introduces four techniques for calculating the volume of various geometric objects. Two techniques are associated with solids of revolution, where an object is cut into flat slices or concentric cylindrical shells and summed over the object’s extent using a single integral. The third technique employs two integrals where the first computes the area of a slice through a volume, and the second sums these areas over the object’s extent. The fourth technique employs three integrals to sum the volume of an object. We start with the slicing technique.