To start with, compare the circle the diameter we're given would make with the circle the circumference we're given would make:
Since a circumference is π times the diameter, a 'pure' circle of 10 cubits in diameter as we describe the sea as having would be 10π cubits in circumference, or roughly 31.4 cubits.
Now, since the circumference attributed to our sea is only 30 cubits, it represents a smaller circle, which is 30/π or roughly 9.55 cubits in diameter.
Or to tabulate it:
Circle A: ~9.55 cubits diameter, 30 cubits circumference
Circle B: 10 cubits diameter, ~31.4 cubits circumference
Given that, we have two diameters differing by about .45 cubits (about eight inches on an 18-inch cubit--a sizable difference).
Since we know the sea was a physical object and not a circle bounded by an infinitesimal line, we can safely understand that the sea must be of some thickness; on this ground, it would not be unreasonable to take the shorter dimension as the inner measurement, and the longer dimension as the outer measurement, and see where that takes us.
Dividing the difference in the diameters in half, this would make the wall around our sea at least .225 cubits thick--i.e., about four inches on either end of the sea, assuming an eighteen-inch cubit.
Do we have any authority for assuming that this is the case and saying the sea was anything like four inches thick?
A couple of verses after this we have 1 Kings 7:26, which gives it to us outright:
Its thickness was a handbreadth, and its brim was made like the brim of a cup, like the flower of a lily. It held two thousand baths.
A handbreadth as a unit of measurement is generally given as between three and four inches.
(The 'Number Pi in the Bible' site linked elsewhere gives as its rebuttal to this sort of argument the statement "The writer makes sure that no question remains: both the diameter and the circumference are taken over-all." - though I'm not sure on what basis he sees that.)