Pappus theorem and area of a revolution surface.

Question

Let $y=f(z)$ be a function. How can I calculate the area of the surface obtained rotating the function along the $z$ axis, where y is the revolution torus? Is it possible to do it using Pappus formula $$ A= 2\pi \int y \sqrt{1+\stackrel{\cdot}{y}^2}dz\,\,\, ?$$ Thank you!