In mathematics, a dome is a closed geometrical surface which can be obtained by sectioning off a portion of a sphere with an intersecting plane. It consists of two parts: (1) a flat disk, which is joined to (2) a convex surface whose curvature is uniform and which has a circular boundary: this boundary joins with the rim of the disk. The disk can be referred to as the dome's "base". Mathematics is often defined as the study of topics such as quantity, structure, space, and change. ... Geometry (Greek γεωμετρία; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. ... An open surface with X-, Y-, and Z-contours shown. ... A sphere is a perfectly symmetrical geometrical object. ... Look up plane in Wiktionary, the free dictionary. ... A disc (or disk) is anything that resembles a flattened cylinder in shape. ... Curvature is the amount by which a geometric object deviates from being flat. ...

A pair of parameters are enough to describe a dome: (1) its diameter and (2) its height. The diameter refers to the size of the base, whereas the height refers to the perpendicular distance between the center of the base and the center of the concavity. For the geometric term, see diameter. ... Height is a measurement of the distance from the bottom to the top of something which is upright. ...

The dome's convex region, which may be referred to here as "ceiling" (in an analogy with architecture) has a radius of curvature r_c given by Curvature is the amount by which a geometric object deviates from being flat. ...

where d is the diameter and h is the height.

The kind of dome described so far is a spherical dome, though there are variants, such as the spheroidal dome, obtained by sectioning off a portion of a spheroid so that the resulting dome is symmetrical (having an axis of rotation), and likewise the ellipsoidal dome derived from the ellipsoid. A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. ... The axis of rotation of a rotating body is a line such that the distance between any point on the line and any point of the body remains constant under the rotation. ... 3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ...

The surface area of a spherical dome's ceiling is

and the dome's volume is given by