Surface area Surface area The surface area of a solid object is a measure of the total area that the surface of the 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
Solid of revolution suitable integral. The disk method is used when the slice that was drawn is "perpendicular to" the axis of revolution; i.e. when integrating "parallel to" the axis of revolution. The volume of the solid formed by rotating the area between the curves of and and the lines and about the -axis is given by If (e.g. revolving an area between the curve and the -axis), this reduces to: The method can be visualized by considering a thin horizontal rectangle at between on top and on the bottom, and revolving it about the -axis; it forms a ring (or disc in