Sphere segment calculation

Description of the calculation of sphere segments

Spherical Segment

The segment of a sphere is determined by its heighte \(h\) and the segment radius \(a\).

Calculate surface of spherical cap \(S\)

\(\displaystyle S=2·π·r·h\)

Calculate volume of spherical cap \(V_s\)

\(\displaystyle V_s=\frac{1}{3}·π·h^2·(3·r - h)\)

Calculate spherical cap height \(h\)

\(\displaystyle h=r-\sqrt{r^2 -a^2}\)

Calculate spherical cap Radius \(a\)

\(\displaystyle a= \sqrt{h(2· r -h)}\)

\(\displaystyle a= \sqrt{r^2-(r -h)^2}\)

Calculate spherical cap base area \(A\)

\(\displaystyle A=a^2 ·π\)

Calculate surface cap and base \(S_{Seg}\)

\(\displaystyle S_{Seg}=S+A\)