Surface area representing a cell as an idealized sphere of radius "r", the volume and surface area are, respectively, "V" = 4/3 π "r"; "SA" = 4 π "r". The resulting surface area to volume ratio is therefore 3/"r". Thus, if a cell has a radius of 1 μm, the SA:V ratio is 3; whereas if the radius of the cell is instead 10 μm, then the SA:V ratio becomes 0.3. With a cell radius of 100, SA:V ratio is 0.03. Thus, the surface area falls off steeply with increasing volume. Surface area The surface area of a solid object is a
Solid angle of a planar triangle is equal to "", for the sum of the four internal solid angles of a tetrahedron as follows: where ranges over all six of the dihedral angles between any two planes that contain the tetrahedral faces OAB, OAC, OBC and ABC. A useful formula for calculating the solid angle subtended by the triangular surface ABC where formula_17 are the vector positions of the vertices A, B and C has been given by Oosterom and Strackee (although the result was known earlier by Euler and Lagrange): where denotes the scalar triple product of the three vectors; When