spherical sector [′sfir·ə·kəl ′sek·tər]
Spherical Sector
(mathematics)
A solid formed by rotating a sector of a circle about a diameter of the circle; the diameter may contain one of the radii bounding the circular sector or it may lie outside the circular sector.
Spherical Sector
(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.
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