Description of the calculation of sphere segments
The segment of a sphere is determined by its heighte \(h\) and the segment radius \(a\).
\(\displaystyle S=2·π·r·h\)
\(\displaystyle V_s=\frac{1}{3}·π·h^2·(3·r - h)\)
\(\displaystyle h=r-\sqrt{r^2 -a^2}\)
\(\displaystyle a= \sqrt{h(2· r -h)}\)
\(\displaystyle a= \sqrt{r^2-(r -h)^2}\)
\(\displaystyle A=a^2 ·π\)
\(\displaystyle S_{Seg}=S+A\)
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