rate of growth of a leaking oil tank

A gas tank on a dock has a small puncture and is leaking gas at the rate of $\displaystyle 1cm^3/min$ into a lake. It forms a circular slick that is 1mm thick on the surface of the water.

so as a function of time the amount of gas leaked is $\displaystyle V=1cm^3 * m$ but i also have to state the radius as a function of volume and as a function of time. im supposing i should approach the radius as volume as a very short cylinder, which i think i would be $\displaystyle r=\sqrt{\frac{\pi*h}{V}}$ and as a function of a time as $\displaystyle r=\sqrt{\frac{\pi*h}{1cm^3 * min}}$

this is my first time attempting a question like this and im not even sure its in the correct forum so any advice would be appreciated :)