Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 + y2.

The area of the part of the sphere that lies inside the paraboloid is 100 and this can be determined by doing the integration.

Given :

First, parameterize S as given below:

In the above expression the value of and

Now, evaluate the surface integral as given below:

  --- (1)

Now, the value of is given by:

Now, substitute the value of in the expression (1).

Simplify the above integral in order to determine the area of the part of the sphere.

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