rR=4;rr=2;

ParametricPlot3D[{(rR+rr Cos[s])Cos[t],(rR+rr Cos[s])Sin[t],rr Sin[s]},{t,0,2 Pi},{s,0, 2 Pi}]

Clear[rR,rr]

FullSimplify[Cross[D[{(rR+rr Cos[s])Cos[t],(rR+rr Cos[s])Sin[t],rr Sin[s]},t],D[{(rR+rr Cos[s])Cos[t],(rR+rr Cos[s])Sin[t],rr Sin[s]},s]]]

FullSimplify[{rr Cos[s] (rR+rr Cos[s]) Cos[t],rr Cos[s] (rR+rr Cos[s]) Sin[t],rr (rR+rr Cos[s]) Sin[s]}.{rr Cos[s] (rR+rr Cos[s]) Cos[t],rr Cos[s] (rR+rr Cos[s]) Sin[t],rr (rR+rr Cos[s]) Sin[s]}]

Integrate[Integrate[rr (rR+rr Cos[s]),{s,0, 2 Pi}],{t,0,2 Pi}]