Annulus is a Latin word meaning a ring. In mathematics annulus refer to the region between two concentric circles. Real Life examples of annulus are a circular path round a circular region, a circular running track etc. In a pipe or a tube with circular cross sections, the material is contained in the annular Cylinder formed.


Annulus Area

Area of annulus = Area of outer circle - Area of inner circle.
                          = πR2 - πr2 = π(R2 - r2) sq.units

Solved Example

Question: A jogging path of width 4ft goes around a circular play area for children. The diameter of the play area is 90 ft. The administration is considering relaying the tiles in jogging path. if the cost of laying is quoted as 15 dollars per sq.ft, find the total cost for relaying tiles on the jogging path.
Annulus Area Example
Solution:
 
The area of the path can be calculated using annulus area formula
where R = radius of the outer circle = 45 + 4 = 49 ft   and r = radius of the play area = 45 ft
Area of the jogging path = π(R2 - r2)
                                       = π(492 - 452) = 1181.24 sq ft.
Cost of relaying per sq ft = 15 dollars
Total cost of relaying tiles on jogging path = 1181.24 x 15 = 17,718.60 dollars.