# Area of a Circular Ring or Annulus

__Annulus__**:**

A circular ring (annulus) is plane figure bounded by the circumference of two concentric circles of two different radii. The area of a circular ring is found by subtraction the area of small circle from that of the large circle. The examples of annulus are the area of a washer and the area of a concrete pipe.

If and , and stands for the areas and the radii of two circles and for the area of the ring, the

**i.e.**to find the area of a ring (or annulus), multiply the product of the sum and the difference of the two radii by in first figure.

**Note:**Rule holds good even when circles are not concentric as in second figure.

__Example__:

A path cm wide, surrounds a circular lawn whose diameter is cm. Find the area of the path.

__Solution__:

Given that

Radius of inner circle cm

Radius of outer circle cm

Area of path

Square cm

__Example__:

The areas of two concentric circles are square cm and square cm respectively. Find the width of the ring.

__Solution__:

Let and be the radii of the outer and inner circles respectively. Let be the width of the ring then

Area of the outer circle square cm

or cm

Area of the inner circle square cm

Hence, width of ring cm