# Annulus Formula

## Annulus Formula

An annulus is a two-dimensional flat object with a circular shape formed by two concentric circles. The Annulus Formula is the region or area generated between these two concentric rings. Because it is a circular flat shape, the edges are two circles with the same centre. It is a round disc with a circular hole in the centre.

The Annulus Formula  is derived from the Latin word ‘annuli,’ which means “little rings.” The annulus has a flat and round form with a hole in the middle, similar to a throw ring or a circular disc. Consider the illustration below, which depicts two circles: a tiny circle, also known as an inner circle, and a large circle, also known as an outer circle. The centre of both circles is shown by the red point. An annulus is a shaded-coloured region between the boundaries of these two circles.

The Annulus Formula area is the enclosed region between the two concentric circles, defined as the ring-shaped space. Students need the area of both the inner and outer circles to compute the size of the annulus. An annulus’ dimensions are specified by the two radii R and r, which are the radii of the outer and inner rings, respectively. Once they have the radii of both circles, students can compute the area by subtracting the area of the tiny circle from the area of the huge circle.

As a result, the formula for calculating the Annulus Formula area is:

Area of Outer Circle = πR2

Area of Inner Circle = πr2

Area of Annulus Formula = Area of Outer Circle – Area of Inner Circle

where ‘R’ is the radius of the outer circle

The radius of the annulus’ inner circle is known as ‘r.’

This Extramarks page will explain what the Annulus Formula is, as well as the area and examples.

The circle is recognised as a basic idea not just in mathematics, but also in many other disciplines. Students know from its description that a circle is a planar shape made up of points that are all the same distance apart from one another.

### Solved Example

Find the area of the path, where a path is 14 cm wide and surrounds a circular lawn whose diameter is 360 cm.

Width of the path = 14 cm

The Diameter of the inner circle is 360 cm.

The radius of inner circle (r) = 360/2 = 180 cm

Radius of outer circle is (R) = 180 + 14 = 194 cm

A =π(R2–r2)

= 3.142 (R + r)(R – r)

= 3.142 (194 + 180) (194 – 180)

= 3.142×374×14

= 16451.512 cm2