# 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 $$S_{Seg}$$

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