Segment

A segment on a plane is a plane figure included between a curve and a chord of it. The area of a segment of a circle (a circular segment) is $S=r^2(\theta-\sin\theta)/2$, where $r$ is the radius of the circle and $r\theta$ is the length of the arc.

A segment in space is a part of a solid bounded by a plane and the part of the surface cut off by the plane. The volume $V$ of a segment of a ball (a spherical segment) is given by $V=\pi h^2(3R-h)/3$, where $R$ is the radius of the ball and $h$ is the height of the segment. The area $S$ of the curved surface of a segment of a ball is given by $S=2\pi Rh$.

Comments

Of course, a line segment is the part of a line between two of its points, or (in real projective geometry) one of the two parts into which two points decompose the line through them [a1], pp. 176-177.

For a segment in space see also [a2], p.245.

References

[a1]	H.S.M. Coxeter, "Introduction to geometry" , Wiley (1989)
[a2]	H. Lamb, "Infinitesimal calculus" , Cambridge (1924)