# How do you find the surface area of the part of the circular paraboloid #z=x^2+y^2# that lies inside the cylinder #x^2+y^2=1#?

##### 1 Answer

Mar 24, 2015

I assume the following knowledge; please ask as separate question(s) if any of these are not already established:

- Concept of partial derivatives
- The area of a surface,
#f(x,y)# , above a region R of the XY-plane is given by#int int_R sqrt((f_x')^2 + (f_y')^2 +1) dx dy# where

#f_x'# and#f_y'# are the partial derivatives of#f(x,y)# with respect to#x# and#y# respectively. - In converting the integral of a function in rectangular coordinates to a function in polar coordinates:
#dx dy rarr (r) dr d theta#

If

then

The Surface area over the Region defined by

Converting this to polar coordinates (because it is easier to work with the circular Region using polar coordinates)