What is described as the area between the arc of a curve and its long chord?

The area between the arc of a curve and its long chord is referred to as a segment. In surveying and geometry, a segment specifically pertains to the section of a circle that is bound by a chord and the arc that lies above it. This is crucial in calculations related to curves in road and railway design, as it helps surveyors and engineers understand the geometric properties of circular arcs.

Regarding the context of the other options, a fillet typically refers to a rounded corner or edge used in design, often to prevent sharp edges or to facilitate smoother transitions. A sector is a portion of a circle that is bounded by two radii and the arc connecting them, representing a slice of the circle rather than the area between a chord and an arc. Volume, on the other hand, deals with three-dimensional space rather than the two-dimensional area described by the segment. Thus, the segment is the precise term that describes the area of interest in this question.