that lies above the unit circle.
1. Find the surface area of the paraboloid
that lies above the unit circle.
Answer:
Because
and
you would get the following integral for surface area:
To make this problem easier to solve we can convert into polar coordinates:
2. Find the surface area S of the portion of the hemisphere
that lies above the region R bounded by the circle
Answer:
First find the partial derivates of
We then set up the surface area integral and simplify:
Next we convert to polar coordinates and solve:
