# 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 subtracting the area of the small circle from that of the large circle. An example of an annulus is the area of a washer and the area of a concrete pipe.

If and , and stand 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 the 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 with a diameter of cm. Find the area of the path.

__Solution__:

Given that

Radius of inner circle cm

Radius of outer circle cm

the 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

the area of the outer circle square cm

or cm

the area of the inner circle square cm

Hence, the width of the ring cm