Description and formulas for the calculation of sphere sectors
The sector of a sphere corresponds to a sphere segment which has a cone formed by the center of the sphere and the base of the cap. The sector of a sphere is determined by its height \(h\) and the parallel circle radius \(a\).
\(\displaystyle S=2·π·r·h\)
\(\displaystyle V_s=\frac{2}{3}·π·r^2· h\)
\(\displaystyle h=r-\sqrt{r^2 -a^2}\)
\(\displaystyle a= \sqrt{h(2· r -h)}\)
\(\displaystyle a= \sqrt{r^2-(r -h)^2}\)
\(\displaystyle S_L=a· r ·π\)
\(\displaystyle S_{Seg}=S+S_L\)