The curved surface area and the total surface area of a cylinder are in the ratio 1 : 3. If total surface area is 616 cm2 then find the volume of water which it can store.

Given:
– The ratio of the curved surface area (CSA) to the total surface area (TSA) of a cylinder is 1:3.
– The total surface area (TSA) is 616 cm².

1. The formula for the TSA of a cylinder is \(2\pi rh + 2\pi r^2\), and the formula for the CSA is \(2\pi rh\).

Given the ratio:
\[ \frac{2\pi rh}{2\pi rh + 2\pi r^2} = \frac{1}{3} \]

2. Solving this equation for \(h\):
\[ 4\pi rh = 2\pi r^2 \]
\[ 2h = r \] (Equation A)

3. Using the given TSA (616 cm²):
\[ 2\pi rh + 2\pi r^2 = 616 \] (Equation B)

4. From equations A and B:
\[ \pi r^2 + 2\pi r^2 = 616 \]
\[ 3\pi r^2 = 616 \]
\[ r^2 = \frac{616 \times 7}{22 \times 3} \]
\[ r^2 = 28 \times \frac{7}{3} \]
\[ r = \frac{14}{\sqrt{3}} \text{ cm} \]

5. Using equation A to find \(h\):
\[ h = \frac{7}{\sqrt{3}} \text{ cm} \]

6. The volume of the cylinder is:
\[ V = \pi r^2 h \]
\[ V = \frac{22}{7} \times \frac{14}{\sqrt{3}} \times \frac{14}{\sqrt{3}} \times \frac{7}{\sqrt{3}} \]
\[ V = \frac{4312}{3\sqrt{3}} \text{ cm}^3 \]

Conclusion:
The volume of water the cylinder can store is \(\frac{4312}{3\sqrt{3}} \text{ cm}^3\).