SPHERE (Lat. sphaya, from Gk. eibarpa, sphaira, ball, globe; connected with Lith.
ball of dung, and perhaps with Skt. splint., to hasten, steeteb out). A solid bounded by a sur face every point of which is at a given distance from a fixed point. The given distance is called the radius and the fixed point the centre of the sphere. A spherical surface may be generated by revolving a semi-circumference about its diam eter. Sections of a sphere made by planes are circles. if the plane passes through the centre of the sphere, the circle is a great circle, other wise a small circle of the sphere. if the seg ments into which a plane divides a sphere are un equal, the smaller is called the minor and the lazger the major segment. That portion of the spherical surface which is included between two parallel planes which cut or touch the surface is called a zonr. The portion of a sphere gener ated by the revolution of a circular sector about any diameter of its circle as an axis is called a spherical sector.
The surface of a sphere is equal to four times the area of a great circle of the sphere, or r being the radius of the sphere. Its volume is 1:11-e. The rectangular equation of a sphere. the origin being at the centre, is + + r'. (See ('O6RDYNATES. ) (For the formulas for areas and volumes relating to zones, segments. and sectors, see MENSURA TION.) A remarkable property of the sphere is that its surface is equal to the curved surface of the circumscribed cylinder and its volume is two thirds of that of the cylinder, a property said to have been discovered by Archimedes (q.v.). If a sphere and a double cone he inscribed in an equi lateral cylinder, the sphere and the volume be tween the cone and the cylinder are Cavalieri bodies. See CAVALIERI.