Volume as the disk radius, the volume of the sphere can be calculated as Now Combining yields formula_15 This formula can be derived more quickly using the formula for the sphere's surface area, which is formula_16. The volume of the sphere consists of layers of infinitesimally thin spherical shells, and the sphere volume is equal to The cone is a type of pyramidal shape. The fundamental equation for pyramids, one-third times base times altitude, applies to cones as well. However, using calculus, the volume of a cone is the integral of an infinite number of infinitesimally thin circular disks of thickness
Ideal surface Ideal surface An ideal solid surface is flat, rigid, perfectly smooth, and chemically homogeneous, and has zero contact angle hysteresis. Zero hysteresis implies the advancing and receding contact angles are equal. In other words, only one thermodynamically stable contact angle exists. When a drop of liquid is placed on such a surface, the characteristic contact angle is formed as depicted in Fig. 1. Furthermore, on an ideal surface, the drop will return to its original shape if it is disturbed. The following derivations apply only to ideal solid surfaces; they are only valid for the state in which the interfaces