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| PAGE: 1040 | SET: Exercises | PROBLEM: 9 |
The equation of the cylinder is 
and the plane is 
.
The radius of the cylinder is 1 and center at origin.
The radius of the cylinder varies from 0 to 1.
If a smooth parametric surface S is given by the 
then the surface area of S is 
.
Consider 
.
Evaluate 
.
Apply partial derivative with respect to x.
Evaluate 
.
Apply partial derivative with respect to y.
Substitute 
and 
in the surface area formula.
Convert the area from rectangular to polar coordinates.
Region bounded by the cylinder is 
.
Area of the surface is 
.
Area of the surface is 
.
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