Let r cm be the radius of the base and h cm be the height of the cylinder,
Then, total surface area of cylinder = 2πr (r + h)
Curved surface area of cylinder = 2πrh
We have,
Curved surface area = 1/3(Total surface area) = 1/3 x 462 cm^{2} = 154 cm^{2}
⇒ 2πrh = 154
Also, 2πrh + 2πr^{2} = 462 ⇒ 154 + 2πr^{2} = 462
⇒ 2πr^{2 }= 462 - 154 = 308 cm^{2}
2 x 22/7 x r^{2} = 308
⇒ r^{2 }= 308 x 7/2 x 22 = 7^{2 }⇒ r = 7 cm
Again 2πrh = 154 ^{ }⇒ 2 x 22/7 x 7 x h = 154
⇒ h = 154/2 x 22 = 7/2 cm
Volume of the cylinder = πr^{2}h
= 22/7 x 7 x 7 x 7/2 = 539 cm^{3}