# Spherical Segment of One Base

## Spherical Segment of One Base

Each of the two portions of a sphere obtained by cutting the sphere with a plane.

The outer layer of the spherical segment of one base is called a spherical cap.

### Formula

The lateral area A of a spherical cap of radius r and height h is given by: A = $$2πrh$$.

The volume V of a spherical segment is obtained by using the formula : V = $$\dfrac{πh(3q^{2} + h^{2})}{6}$$ where $$h$$ is the height of the segment and $$q$$ is the radius of the small circle.

The Pythagorean theorem can be applied to the right triangle shown in the figure above, in which $$\left ( R-h \right )^{2}+r^{2}=R^{2}$$, to deduce that $$r^{2}=2Rh-h^{2}$$, where the radius $$r$$ of the spherical segment has a value of $$\sqrt{h(2R-h)}$$.The preceding formula to calculate the volume of a spherical segment as a function of the height $$h$$ and the radius $$R$$ of the sphere becomes: $$V = \dfrac{\pi h^2 (3r-h)}{3}$$.