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
Surface energy radius formula_1 and length formula_2 at high temperature and a constant uniaxial tension formula_3, then at equilibrium, the variation of the total Helmholtz free energy vanishes and we have where formula_5 is the Helmholtz free energy and formula_6 is the surface area of the rod: Also, since the volume (formula_8) of the rod remains constant, the variation (formula_9) of the volume is zero, i.e., Therefore, the surface energy density can be expressed as The surface energy density of the solid can be computed by measuring formula_3, formula_1, and formula_2 at equilibrium. This method is valid only if the solid is