HOW TO FIND THE AREA OF A RING OR WASHER

A ring or a washer is a combination of two circles one inside thee other. So we have to deal with two radii and hence to find areas of both the circles. Then subtract the area of smaller circle from the larger ones to get the area between both the circles with is actually the area of the ring or washer.

In the picture given given above we can find the area of the washer as shown below:

 Area of smaller circle:
Given radius for the smaller (inner) circle r = 3 cm
Area of smaller circle = pi x radius x radius = 3.14 x 3 x 3 = 3.14 x 9 = 28.26 sq.cm   
Hence the area of the inner circle is 28.26 square centimeters.
 

Area of larger circle:
Given radius for the larger (outer) circle is R = 5 cm
Area of the larger circle = Pi x radius x radius = 3.14 x 5 x 5 = 3.14 x 25 = 78.50 sq.cm
Hence the area of the outer (larger) circle is 78.50 square centimeters.   

Area of the Washer:  Once you have calculated the area of both the circles (inner and outer)  using given radii, the next step is to find the area of the washer by  subtracting the above results. The area of the washer is equal to the  area between both the circles. 

 
Area of the washer = Area of outer circle - Area of the inner circle  = 78.50 - 28.26 = 50.24 sq.cm 

Hence the area of the ring (circular washer) with outer radius of 5 cm and the inner radius of 3 cm found to be 50.24 sq. cm.