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

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