Annulus Formula

An Annulus is a ring-shaped object, bounded by the circumference of two concentric circles of two different radius. An Annulus is much like the throw-ring.. One way to think of it is a circular disk with a circular hole in it. The outer and inner circles that define the ring are concentric that shares a common center point.
Annulus Formula

The dimensions of an annulus are defined by the two radii R, r, which are the radii of the outer ring and the inner ‘hole’ respectively. The area of a circular ring can be found by subtraction the area of small circle from that of the large circle.

Here are formulas to find Area of Annulus
Annulus Formula

Annulus Formula

Annulus Formula

Where,
A = Area of Annulus
R = Outer radius
r = Inner radius
(Pi) $\pi$ = is approximately 3.142

Example 1:
Find the area of the path, where a path is 14cm wide, surrounds a circular lawn whose diameter is 360cm.
Solution:
Given
Diameter of inner circle is 360cm, means the radius (r) is 180cm
Radius of outer circle is (R) = 180 + 14 = 194cm

A = $\pi$ ($R^{2}$ – $r^{2}$)
= 3.142 ($R^{2}$ + $r^{2}$) ($R^{2}$ – $r^{2}$)
= 3.142 (194 + 180) (194 – 180)
= 3.142 $\times$ 374 $\times$ 14
= 16451 cm2


Practise This Question

In a closed container of constant volume, the pressure of water exhibits an interesting dependence on temperature - 

The point D (273.16 K,0.006 atm) is called the triple point, Tp, of water, where all there phases coexist. What is the observed phase change when the temperature is increased from -100C to +100C, while maintaining a constant pressure of 0.006 atm?