As an example of how you might begin, take one litre as the volume.

How many cubic centimetres is that ?

If the radius was 1 cm, 2 cm, 3 cm, etc. what would the height
be each time ?

And how long would the 'slope length' be in each case ?

How do you calculate the curved surface area using those things ?

When was the curved surface area least ?

Can you refine your answer with more precise values tried for the radius length ?

Could a spreadsheet help with the repeated calculation ?