Solid angle surface area of a spherical cap is always equal to the area of a circle whose radius equals the distance from the rim of the spherical cap to the point where the cap's axis of symmetry intersects the cap. In the diagram this radius is given as: Hence for a unit sphere the solid angle of the spherical cap is given as: When = , the spherical cap becomes a hemisphere having a solid angle 2. The solid angle of the complement of the cone (picture a melon with the cone cut out) is clearly: This is also the solid
Finite volume method tensor. Again we can sub-divide the spatial domain into finite volumes or cells. For a particular cell, formula_42, we take the volume integral over the total volume of the cell, formula_43, which gives, On integrating the first term to get the "volume average" and applying the "divergence theorem" to the second, this yields where formula_46 represents the total surface area of the cell and formula_47 is a unit vector normal to the surface and pointing outward. So, finally, we are able to present the general result equivalent to (8), i.e. Again, values for the edge fluxes can be reconstructed by