The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2.

Let r cm be the radius and h cm be the length of the cylinder. The curved surface area and the total surface area is 1:2.

The total surface area is 616 cm2.

The curved surface area is the half of 616 cm2, i.e. 308 cm2​.

Curved area = 2πrh

$r^{2}=\frac{308}{2 \times \frac{22}{7}}$

r = 7 cm

$h=\frac{308}{2 \times \pi \times 7}=7 \mathrm{~cm}$

Then, the volume of the cylinder can be calculated as follows:

$V=\frac{22}{7} \times 7^{2} \times 7=1078$

Hence, it is obtained that the volume of the cylinder is 1078 cm3.