Spherical Segment
Definition, properties, and formulas for the spherical segment (spherical cap with base)
Definition and Geometry
A spherical segment is the part of a sphere cut off by a plane. Its shape is dome-like, and its base is a circle.
A hemisphere is a special spherical segment where the cutting plane passes through the center. The curved outer part is often called the spherical cap.
Main parameters:
- r = sphere radius
- h = segment height
- a = base circle radius
Sign rule for ± formulas:
Use − if the segment is smaller than a hemisphere,
and use + if the segment is larger than a hemisphere.
Formulas
Volume
Segment height
Segment radius
Cap surface area
Base area
Total segment surface
Sphere radius
Vs = πh²(3r − h)/3
S = 2πrh
A = πa²
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