zone which encompasses all of the Tropics. Generalizations Sections of other solids The spheroidal dome is obtained by sectioning off a portion of a spheroid so that the resulting dome is circularly symmetric (having an axis of rotation), and likewise the ellipsoidal dome is derived from the ellipsoid. Hyperspherical cap Generally, the -dimensional volume of a hyperspherical cap of height and radius in -dimensional Euclidean space is given by: where (the gamma function) is given by . The formula for can be expressed in terms of the volume of the unit n-ball and the hypergeometric function or the regularized incomplete beta function as , and the area formula can be expressed in terms of the area of the unit n-ball as , where . Earlier in (1986, USSR Academ. Press) the following formulas were derived: , where , . For odd . Asymptotics It is shown in that, if and , then where is the integral of the standard normal distribution. A more quantitative bound is . For large caps (that is when as ), the bound simplifies to . See also Circular segment — the analogous 2D object Solid angle — contains formula for n-sphere caps Spherical segment Spherical sector Spherical wedge References Further reading External links Derivation and some additional formulas. Online calculator for spherical cap volume and area. Summary of spherical formulas. Spherical geometry