An Annulus is a ring-shaped object, bounded by the circumference of two concentric circles of two different radii. 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](https://cdn1.byjus.com/wp-content/uploads/2016/04/Annulus-Formula.png)
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 a small circle from that of the large circle.
Here are formulas to find Area of Annulus.
\(\begin{array}{l}\begin{aligned} A &=\pi\left(R^{2}-r^{2}\right) \\ R &=\sqrt{r^{2}+\frac{A}{\pi}} \\ r &=\sqrt{R^{2}-\frac{A}{\pi}} \end{aligned}\end{array} \)
Where,
A = Area of Annulus
R = Outer radius
r = Inner radius
(Pi) \(\begin{array}{l}\pi\end{array} \)Â = is approximately 3.142
Solved Example
Example :Â Find the area of the path, where a path is 14 cm wide, surrounds a circular lawn whose diameter is 360 cm.
Solution:
Given,
Width of the path = 14 cm
Diameter of the inner circle is 360 cm.
Radius of inner circle (r) = 360/2 = 180 cm
Radius of outer circle is (R) = 180 + 14 = 194 cm
A =
\(\begin{array}{l}\pi\end{array} \)
(\(\begin{array}{l}R^{2}\end{array} \)
– \(\begin{array}{l}r^{2}\end{array} \)
)= 3.142 (R + r)(R – r)
= 3.142 (194 + 180) (194 – 180)
= 3.142Â
\(\begin{array}{l}\times\end{array} \)
374Â \(\begin{array}{l}\times\end{array} \)
14= 16451.512 cm2
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