Surface-area-to-volume ratio Surface-area-to-volume ratio 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. 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
Surface area but not on its position and orientation in space. This means that surface area is invariant under the group of Euclidean motions. These properties uniquely characterize surface area for a wide class of geometric surfaces called "piecewise smooth". Such surfaces consist of finitely many pieces that can be represented in the parametric form with a continuously differentiable function formula_4 The area of an individual piece is defined by the formula Thus the area of "S" is obtained by integrating the length of the normal vector formula_6 to the surface over the appropriate region "D" in the parametric "uv" plane. The