Spherical Sector
Definition, properties, and formulas for spherical sector calculations
Definition and Properties
A spherical sector is the 3D body enclosed by a spherical cap and the cone formed by connecting the cap boundary circle with the sphere center.
It can be described by sphere radius r, base radius a, and cap height h. Any two of these values determine the third.
Main variables:
- r = sphere radius
- a = base circle radius
- h = cap height
- θ = opening angle at the sphere center
Sign rule for ± formulas:
Use − if the cap is smaller than a hemisphere and + if it is larger.
Formulas
Segment radius a
Segment height h
Sphere radius r
Sector volume
Cap surface SK
Cone surface SL
Total surface SSec
V = 2πr²h/3 SK = 2πrh SSec = SL + SK
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