I am wondering if someone could help me with the following? I am supposed to find the area of the finite part of the paraboloid y = x^2+z^2 that's cut off by the plane y = 25. Now, wouldn't this be the same as the paraboloid z = x^2+y^2 that's cut off by the plane z = 25?
So, if that's right, then the surface area is ∫∫√((dz/dx)^2+(dz/dy)^2+1).
This seems easier to do in polar coordinates, so we basically have the following:
∫∫(1+4r^2)? And, r would be from 0 to 5, and 0≤θ≤2*pi?
Am I doing something wrong here? Or, how do I "project" the surface unto the x-z plane? Thanks!