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also see Defining Geometric Figures

 Sphere

    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

 

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

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