(or sector of a sphere), the geometric solid generated by the rotation of a sector of a circle about one of the radii bounding the sector (Figure 1,a) or about a diameter that does not intersect the arc bounding the sector (Figure 1,b).

Figure 1

The volume of both types of spherical sector is V = 2πR²h/3. The area of the surface of the first type of spherical sector is S₁ = πR(2h + a); the corresponding area for the second type of spherical sector is S₂ = πR(2h + a + b). Here, R is the radius; h is the length of the projection, onto the axis of rotation, of the chord joining the endpoints of the arc; and a and b are the distances of the endpoints from the axis.