Spherical sector
Encyclopedia
In geometry
, a spherical sector is a portion of a sphere
defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap
and the cone formed by the center of the sphere and the base of the cap.
If the radius of the sphere is denoted by r and the height of the cap by h, the volume
of the spherical sector is
If the radius of the base of the cap is denoted by a, the surface area
of the spherical sector is
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a spherical sector is a portion of a sphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap
Spherical cap
In geometry, a spherical cap is a portion of a sphere cut off by a plane. If the plane passes through the center of the sphere, so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere....
and the cone formed by the center of the sphere and the base of the cap.
If the radius of the sphere is denoted by r and the height of the cap by h, the volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
of the spherical sector is
If the radius of the base of the cap is denoted by a, the surface area
Surface area
Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra the surface area is the sum of the areas of its faces...
of the spherical sector is
See also
- Circular sectorCircular sectorA circular sector or circle sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. In the diagram, θ is the central angle in radians, r the radius of the circle, and L is the arc length of the...
— the analogous 2D object. - Spherical capSpherical capIn geometry, a spherical cap is a portion of a sphere cut off by a plane. If the plane passes through the center of the sphere, so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere....
- Spherical segmentSpherical segmentIn geometry, a spherical segment is the solid defined by cutting a sphere with a pair of parallel planes.It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum...
- Spherical wedgeSpherical wedgeIn geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune . The angle between the radii lying within the bounding semidisks is the dihedral angle of the wedge α...