Spherical cap
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle), so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere. Volume and surface area The volume of the spherical cap and the area of the curved surface may be calculated using combinations of The radius of the sphere The radius of the base of the cap The height of the cap The polar angle between the rays from the center of the sphere to the apex of the cap (the pole) and the edge of the disk forming the base of the cap If denotes the latitude in geographic coordinates, then , and . The relationship between and is relevant as long as . For example, the red section of the illustration is also a spherical cap for which . The formulas using and can be rewritten to use the radius of the base of the