Sphere formula:
A three-dimensional figure with all of its points equidistant from its center. Radius: r Diameter: d Surface area: S
Volume: V
S = 4 Pi r2 = Pi d2
V = (4 Pi/3)r3 = (Pi/6)d3
Sector of a Sphere
The part of a sphere between two right circular cones that have a common vertex at the center of the sphere, and a common axis. (The interior cone may have a base with zero radius.)
Radius: r
Height: h
Volume: V
S = 2 Pi rh
V = (2 Pi/3)r2h
Spherical Cap
The portion of a sphere cut off by a plane. If the height, the radius of the sphere, and the radius of the base are equal: h = r (= r1), the figure is called a hemisphere.
Radius of sphere: r
Radius of base: r1
Height: h
Surface area: S
Volume: V
r = (h2 +r12)/(2h)
S = 2 Pi rh
V = (Pi/6)(3r12+h2)h
Segment and Zone of a Sphere
Segment: the portion of a sphere cut off by two parallel planes.
Zone: the curved surface of a spherical segment.
Radius of sphere: r
Radii of bases: r1, r2
Height: h
Surface area: S
Volume: V
S = 2 Pi rh
V = (Pi/6)(3r12+3r22+h2)h
Lune of a Sphere
The curved surface of the intersection of two hemispheres.
Radius: r
Central dihedral angle: theta (in radians), alpha (in degrees)
Surface area: S
Volume enclosed by the lune and the two planes: V
S = 2r2theta = (Pi/90)r2alpha
V = (2/3)r3theta = (Pi/270)r3alpha
A three-dimensional figure with all of its points equidistant from its center. Radius: r Diameter: d Surface area: S
Volume: V
S = 4 Pi r2 = Pi d2
V = (4 Pi/3)r3 = (Pi/6)d3
Sector of a Sphere
The part of a sphere between two right circular cones that have a common vertex at the center of the sphere, and a common axis. (The interior cone may have a base with zero radius.)
Radius: r
Height: h
Volume: V
S = 2 Pi rh
V = (2 Pi/3)r2h
Spherical Cap
The portion of a sphere cut off by a plane. If the height, the radius of the sphere, and the radius of the base are equal: h = r (= r1), the figure is called a hemisphere.
Radius of sphere: r
Radius of base: r1
Height: h
Surface area: S
Volume: V
r = (h2 +r12)/(2h)
S = 2 Pi rh
V = (Pi/6)(3r12+h2)h
Segment and Zone of a Sphere
Segment: the portion of a sphere cut off by two parallel planes.
Zone: the curved surface of a spherical segment.
Radius of sphere: r
Radii of bases: r1, r2
Height: h
Surface area: S
Volume: V
S = 2 Pi rh
V = (Pi/6)(3r12+3r22+h2)h
Lune of a Sphere
The curved surface of the intersection of two hemispheres.
Radius: r
Central dihedral angle: theta (in radians), alpha (in degrees)
Surface area: S
Volume enclosed by the lune and the two planes: V
S = 2r2theta = (Pi/90)r2alpha
V = (2/3)r3theta = (Pi/270)r3alpha
