Surface area of cap using integrals
1. The problem statement, all variables and given/known data
The question asks,
"Find the surface area of the cap cut from the sphere x^2+y^2+z^2=2 by the cone z = sqrt(x^2+y^2)" The answer should be 2pi(2-sqrt(2))
My main problem is not knowing how to get started.
2. Relevant equations
With the example given, it seems we need to find cos(v) first using the equation cos(v) = n*.k/|n|.
3. The attempt at a solution
I found the normal line to be 2xi+2yj+2zk. Using the above formula, I eventually reached the conclusion that z/sqrt(r^2+z^2). I don't know how to use this in an integral and it doesn't follow the example our professor gave us either. Can anyone help?