Spherical Segment Formulas

Posted In: Mathematics

In geometry, a spherical segment is the solid defined by cutting a sphere with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum.

Spherical Segment


Radius of sphere: R
Radius of bases: r1, r2
Height: h
Area of spherical surface: SS
Area of plane end faces: S1, S2
Total surface area: S
Volume: V

  1. $S_S=2πRh$
  2. $S=S_S+S_1+S_2=π(2Rh+r_1^2+r_2^2)$
  3. $V=π/6h(3r_1^2+3r_2^2+h^2)$

Post Tags: Geometry


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