Sphere sector calculation

Description and formulas for the calculation of sphere sectors

Spherical Sector

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 \(a\).

Calculate surface of spherical cap \(S\)

\(\displaystyle S=2·π·r·h\)

Calculate volume of spherical cap \(V_s\)

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

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 surface of the cone \(S_L\)

\(\displaystyle S_L=a· r ·π\)

Calculate surface of the sector \(S_{Seg}\)

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