<P> The surface - area - to - volume ratio, also called the surface - to - volume ratio and variously denoted sa / vol or SA: V, is the amount of surface area per unit volume of an object or collection of objects . In chemical reactions involving a solid material, the surface area to volume ratio is an important factor for the reactivity, that is, the rate at which the chemical reaction will proceed . </P> <P> For a given volume, the object with the smallest surface area (and therefore with the smallest SA: V) is the sphere, a consequence of the isoperimetric inequality in 3 dimensions . By contrast, objects with tiny spikes will have very large surface area for a given volume . </P> <P> 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 </P>

Find the relationship between volume and surface area of a sphere