Surface of revolution never negative, the area is given by If the curve is described by the function , , then the integral becomes for revolution around the -axis, and for revolution around the "y"-axis (using ). These come from the above formula. For example, the spherical surface with unit radius is generated by the curve , , when ranges over . Its area is therefore For the case of the spherical curve with radius , rotated about the -axis A minimal surface of revolution is the surface of revolution of the curve between two given points which minimizes surface area. A basic
BET theory physical adsorption of gas molecules. The total surface area formula_19 and the specific surface area formula_20 are given by where formula_5 is in units of volume which are also the units of the monolayer volume of the adsorbate gas, formula_24 is Avogadro's number, formula_25 the adsorption cross section of the adsorbing species, formula_26 the molar volume of the adsorbate gas, and formula_27 the mass of the solid sample or adsorbent. The BET theory can be derived similarly to the Langmuir theory, but by considering multilayered gas molecule adsorption, where it is not required for a layer to be completed before