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.
Area of annulus = Area of outer circle - Area of inner circle.
= πR2 - πr2 = π(R2 - r2) sq.units
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.
The walls of pipes or tubes form annular cylinders. Hence while finding the material content in a pipe or its weight, the volume of the annular cylinders are found.
Volume of annulus = Volume of the outer cylinder - volume of the inner cylinder
= πR2l - πr2l = πl(R2 - r2) cubic units Where R and r are correspondingly the outer and inner radii and l the length of the pipe.
It is required to compute the annular volume here.
Inner diameter = 4ft. Hence inner radius r = 2ft
Outer radius = r + wall width = 2 + 0.25 = 2.25 ft (3 inches = 0.25 ft)
Height of the cylinder h = 10 ft
Annular volume of the walls = πh(R2 - r2)
= π.10((2.25)2 -22) = 33.38 cubic feet.