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Solved Problems-11

Given that Description: 81947.png, evaluate both sides of the divergence theorem for the volume enclosed by r = 2, z = 0 and z = 5.
Here, Description: 81939.png
Description: 81927.png 
Description: 81918.png
The cylinder has three surfaces as follows.
Description: 81910.png
For the top surface, Description: 81902.png 
Description: 81895.png
For the bottom surface, Description: 81887.png 
Description: 81880.png
For the curved surface, Description: 81872.png 
Description: 81863.png
By addition, total surface area of the closed cylinder is given as,
Description: 81856.png 
Also, Description: 81847.png
Description: 81836.png
Description: 81826.png and hence, divergence theorem is verified.

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