Hi Kevin,
Not sure why Volume does not work, perhaps because the discretization has some imperfections. You could just use calculus
Area of surface of revolution about the x axis
2 Pi NIntegrate[curve[x] Sqrt[1 + D[curve[x], x]^2], {x, 0, 108}]
(* 4048.33 *)
Volume
NIntegrate[Pi curve[x]^2, {x, 0, 108}]
(* 13122.5 *)
