||The Area of the Solid of Intersection of a Sphere and an Ellipsoid, a First Approach
||Skip THOMPSON, Wei-Chi YANG and Vladimir SHELOMOVSKII
In this paper we consider curves of intersection of a fixed ellipsoid and members of a family of spheres with common center and different radii. We use Maple to obtain the exact intersection curve using rectangular coordinates. We then determine the surface area of the portion of the ellipsoid inside the sphere and vice versa. Along the way we discuss several issues of interest to students and instructors of Calculus. We provide examples to illustrate the various possibilities that arise and we provide Maple worksheets that can be used to deal with the rather complicated calculations that must be performed. These worksheets were used with version 14 of Maple to obtain the results reported in this paper.