We have,
Total surface area of cylinder = 616 cm2
Ratio between curved surface area and total surface area of cylinder = 1:2
2πrh / 2πr (h+r) = 1/2
h / (h+r) = 1/2
2h = h+r
h = r
We know, 2πr (h+r) = 616
2πr (r+r) = 616
2πr (2r) = 616
4πr2 = 616
r2 = 616/4π
= 616×7 / 4×22
= 4312 / 88
= 49
r = √49
= 7
Radius = 7cm
Height = 7cm
∴ Volume of cylinder = πr2h
= 22/7 × 7 × 7 × 7
= 1078 cm3