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
Surface-area-to-volume ratio very large surface area for a given volume. The surface-area-to-volume ratio has physical dimension L (inverse length) and is therefore expressed in units of inverse distance. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm and a volume of 1 cm. The surface to volume ratio for this cube is thus For a given shape, SA:V is inversely proportional to size. A cube 2 cm on a side has a ratio of 3 cm, half that of a cube 1 cm on a side. Conversely, preserving SA:V as size increases