Calculating the surface area

Question

I don't know how to solve these problems where there are no visible surfaces:

Calculate the surface area of

\begin{equation*} (x^2+y^2+z^2+R^2-r^2)^2 = 4R^2(x^2+y^2) \end{equation*}

where $$0<r<R$$

Answer 1

This is more a matter of pattern recognition than a matter of calculation. The surface described is that of a torus with major radius $R$ and minor radius $r$, so its surface area (as may be calculated by a number of ways, e.g. Pappus's centroid theorem) is $4\pi^2Rr$.