Approximating the Area of a Circle using Rectangles - Maple Programming Help

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Approximating the Area of a Circle using Rectangles

Main Concept

The area of a circle can be approximated by rectangles. As the number of rectangles approaches infinity the total area of all the rectangles approaches the actual area of the circle.


Using integration, the exact area of the circle can be found. The exact area of a circle is π r2, where r is the radius.


Let r be the radius of the circle, and let n be the number of approximating rectangles.


The height h of each rectangle can be defined as:

h = 2rn


The length lk of the kth rectangle located at height yk can be found from



The area of the kth rectangle is:

Ak = lkh= 2 r2yk2 h  

Therefore the total area of n rectangles is:

Area = 2 k=1nr2yk2h  

In the limit as n  , we get the area of the circle:

Acircle =2 rrr2y2  dy

=  π r2

Adjust the number of rectangles used to approximate the area of the circle:


Number of Rectangles =  


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