# 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 $$S_{Seg}$$

$$\displaystyle S_{Seg}=S+S_L$$