Approximating the Volume of a Sphere using Cylinders - Maple Help

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Approximating the Volume of a Sphere using Cylinders


Main Concept

The volume of a sphere can be approximated by cylinders. As the number of cylinders approaches infinity the total volume of all the cylinder approaches the actual volume of the sphere.


Using integration, the exact volume of the sphere can be found. The exact volume of a sphere is 43π r3, where r is the radius.


Assume the center of the sphere is located at the origin.

Let r be the radius of the sphere, and let n be the number of approximating cylinders.


The height h of each cylinder can be defined as:

h = 2rn

The radius rk of the kth cylinder located at height yk can be found from

rk2 =r2yk2 


The volume of the kth cylinder is thus:

Vk = πrk2h  = πr2yk2h  


Therefore the total volume of n cylinders is:

Volume = k=1nπ r2yk2h 


In the limit as n  , we get the volume of the sphere:

Vsphere = rrπ r2y2 dy

=  43π r3

Change the number of cylinders used to approximate the volume of the sphere:

Number of Cylinders = 



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