Sphere formula in maths

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

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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

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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

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 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

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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