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
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