The definition of a sector ring is a part of an annulus cut off by a circular sector. Its axis of symmetry is the diameter of the annulus, and the area of the sector ring changes with the variation of the sector’s angle. The area of the sector ring can be calculated using the area of the annulus and the area of the sector. The following is the area formula for the sector ring.

The area formula of the sector ring is: S = (n/360) * π * (R² – r²), where n represents the angle of the sector, R denotes the outer diameter of the annulus, and r stands for the inner diameter of the annulus.

The area formula of the sector ring can be used to calculate the area of any part of an annulus that is cut off by a sector. It is widely applied in mathematics, geometry, and engineering. For instance, if a sector ring has an annulus with an outer diameter of 12 cm, an inner diameter of 8 cm, and the sector angle is 45 degrees, then the area of this sector ring is calculated as follows:

S = (45/360) * π * (12² – 8²) = (1/8) * π * 128 = 16π

Therefore, the area of this sector ring is 16π square centimeters.