Spherical Wedge Formulas

Posted In: Mathematics

In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge’s base).

Spherical Wedge

Radius: R
Dihedral angle in degrees: x
Dihedral angle in radians: α
Area of spherical lune: SL
Total surface area: S
Volume: V

  1. $S_L={πR^2}/90\ α=2R^2x$
  2. $S=πR^2+{πR^2}/90\ α=πR^2+2r^2x$
  3. $V={πR^3}/270\ α=2/3R^3x$

Post Tags: Geometry

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