Solid angle orientation formula_9, and distance from the viewer as: where the surface area of a sphere is . The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2, is the area of a spherical cap on a unit sphere For small such that , this reduces to the area of a circle . The above is found by computing the following double integral using the unit surface element in spherical coordinates: This formula can also be derived without the use of calculus. Over 2200 years ago Archimedes proved that the
Specific surface area Specific surface area Specific surface area (SSA) is a property of solids defined as the total surface area of a material per unit of mass, (with units of m/kg or m/g) or solid or bulk volume (units of m/m or m). It is a derived scientific value that can be used to determine the type and properties of a material (e.g. soil or snow). It has a particular importance for adsorption, heterogeneous catalysis, and reactions on surfaces. Values obtained for specific surface area depend on the method of measurement. In adsorption based methods, the size of the adsorbate molecule (the