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
Control volume Control volume In continuum mechanics and thermodynamics, a control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. In an inertial frame of reference, it is a volume fixed in space or moving with constant flow velocity through which the continuum (gas, liquid or solid) flows. The surface enclosing the control volume is referred to as the control surface. At steady state, a control volume can be thought of as an arbitrary volume in which the mass of the continuum remains constant. As a continuum moves through the control volume, the mass entering