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
Volume element formula_25. In coordinates, where formula_27 is the determinant of the metric tensor "g" written in the coordinate system. A simple example of a volume element can be explored by considering a two-dimensional surface embedded in "n"-dimensional Euclidean space. Such a volume element is sometimes called an "area element". Consider a subset formula_28 and a mapping function thus defining a surface embedded in formula_30. In two dimensions, volume is just area, and a volume element gives a way to determine the area of parts of the surface. Thus a volume element is an expression of the form that allows one to