The
surface area of a
solid object is a measure of the total
area that the
surface of an object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of
arc length of one-dimensional curves, or of the surface area for
polyhedra (i.e., objects with flat polygonal
faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a
sphere, are assigned surface area using their representation as
parametric surfaces. This definition of surface area is based on methods of
infinitesimal calculus and involves
partial derivatives and
double integration.