Annulus

An annulus is a shape made up of two circles. The inner region between two concentric circles, or two or more circles with the same centre point, is known as an annulus. A plane shape known as an annulus is created by two concentric circles. Both circles have a common centre. The annulus resembles a ring in shape. With a round hole in the centre, it is regarded as a circular disc. Examples of annular shapes in everyday objects include finger rings, doughnuts, CDs, etc.

What Is An Annulus?

The annulus is the area enclosed between two concentric circles. Concentric circles are those that have the same centre. A circle is a plane shape composed of points that are placed at a uniform distance from a central point. If a circle is encircled by another circle with a radius larger than this circle, then the space or gap between them is the annulus.

What Does An Annulus Look Like?

The annulus is shown in the above illustration by the shaded area.

The illustration above depicts two circles: an inner circle, which is a smaller circle, and an outer circle, which is a larger circle. Point O represents the centre of both the circles.

Area Of Annulus

By calculating the areas of the outer and inner circles, the area of the annulus may be computed. The result is then obtained by deducting the area of the inner circle from the area of the outer circle.

Two circles have the same centre, O, in the illustration above. Let the inner circle's radius be "r," and the outer circle's radius be "R." An annulus is indicated by the shaded area. We must determine the areas of the two circles in order to determine the area of this annulus.

Area of outer circle=\pi R^{2}

Area of inner circle=\pi r^{2}

The area of the annulus equals the difference between the inner and outer circles.

Area of annulus=\pi (R^{2}-r^{2})

This can also be written as, \pi (R+r)(R-r)

Perimeter Of Annulus

The perimeter of a two-dimensional shape is the total linear distance its boundaries cover. As a result, the annulus' perimeter will be equal to the sum of the distances travelled by its outer and inner circles.

If the inner circle's radius is r and the outer circle's radius is R, the annulus's perimeter will be:

2\pi R+2\pi r

This can also be written as, 2\pi (R+r)