Volumes and Cross-Sectional Areas

There is a well-known theorem proved by the classical geometer Pappus that deals with nonparallel cross-sections. England and Miller demonstrate that Pappus' theorem extends to more general curves and to solids with variable cross sections whose centroids do not lie on the given curve "C." All the tools needed are in a standard multivariate calculus course, specifically the calculus of curves in space and the change of variable theorem for multiple integrals.