Manipulate[
 r[u_, v_] := {Cos[u] Sin[v] + a*Sin[v], Sin[u] Sin[v] + b*Cos[v], 
   Cos[c*v]};
 l[w_] := Sqrt[w.w];
 NIntegrate[
   l[Cross[D[r[u, v], u], D[r[u, v], v]]], {u, 0, 2 Pi}, {v, 0, Pi}]
  ParametricPlot3D[r[u, v], {u, 0, 2 Pi}, {v, 0, Pi}], {a, 0, 5}, {b, 
  0, 5}, {c, 1, 10}]