What is the relationship between the water and steam?
I've read that 1 mililiter of water evaporate to 1.6 LITER of steam. Is that true?
To a reasonable approximation steam at 100°C can be treated as an ideal gas. The molar volume of an ideal gas is 22.4 litres, so at 0°C (273K) and one atmosphere 18g of steam occupy 22.4 litres or in more useful units 0.018kg occupy 0.0224 cubic metres. You can work out the volume at 100°C (373K) using Charles' Law, and then calculate the density of steam at 100°C.
There isn't an easy way to calculate the density of water at 100°C, so you'll have to Google it.
Finally calculate the ratio of the two densities, and you have the factor by which the volume expands on boiling. Hopefully I've given enough hints that you can take it from here.