Let the radius and height of the cylinder be r and h, respectively .
Given that, Curved surface area / Total surface area = 1/3
⇒ 2πrh / 2πr(h + r) = 1/3 ⇒ 3h = h + r
⇒ r = 2h = 4cm
∴ volume of cylinder πr2h
= π × (4)^{2 }× 2 = 32π cm^{3 }