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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, then
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
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