surface area of a paraboloid

Hi,

I tried to calculate the area of a paraboloid, say z=x^2+y^2, between z=0 and z=1. I thought that in order to do this calculation, I can think on the paraboloid as consisted of circles with radius sqrt(z), so the surface area would be given by the integral from 0 to 1 on 2*pi*sqrt(z) (the integrand is the perimeter of one circle).

I know for sure that this result is incorrect, because I have seen one exam in which the calculation is carried on by using surface integral of the first kind, which gives a different solution.