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{aligned} A &=pileft(R^{2}-r^{2}right) \ R &=sqrt{r^{2}+frac{A}{pi}} \ r &=sqrt{R^{2}-frac{A}{pi}} end{aligned})

Where,

**A** = Area of Annulus

**R** = Outer radius

**r** = Inner radius

**(Pi) (pi)**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 = $pi$ ($R^{2}$ – $r^{2}$)

= 3.142 (R + r)(R – r)

= 3.142 (194 + 180) (194 – 180)

= 3.142Â $times$ 374Â $times$ 14

= 16451.512 cm^{2}