Sphere
A threedimensional figure with all of its points equidistant
from its center. 
Radius: r
Diameter: d
Surface area: S
Volume: V
S = 4 Pi r^{2}
= Pi d^{2}
V = (4 Pi/3)r^{3}
= (Pi/6)d^{3}


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)r^{2}h


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 (= r_{1}),
the figure is called a hemisphere. 
Radius of sphere: r
Radius of base: r_{1}
Height: h
Surface area: S
Volume: V
r =
(h^{2}+r_{1}^{2})/(2h)
S = 2 Pi rh
V = (Pi/6)(3r_{1}^{2}+h^{2})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: r_{1, }r_{2}
Height: h
Surface area: S
Volume: V
S = 2 Pi rh
V = (Pi/6)(3r_{1}^{2}+3r_{2}^{2}+h^{2})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 = 2r^{2}theta
= (Pi/90)r^{2}alpha
V = (2/3)r^{3}theta
= (Pi/270)r^{3}alpha 

For more about spheres, visit:
Ask Dr. Math:
Volume of a Sphere
Volume of a Hemisphere Using Cavalieri's Theorem
Volume of a Spherical Cap
The Geometry Center: Spheres
Eric Weisstein's World of Mathematics: Sphere
