Problem

We have a cubic room of side $10\rm\ m$, into which no fresh air has been allowed to flow for a week. We register a specific activity of radon $(^{222}\rm Rn)$ of $50\ \rm Bq\,m^{-3}$. Knowing that $^{222}\rm Rn$ is a product in the $^{238}\rm U$ chain, we would like to find the concentration of $^{238}\rm U$ in the walls of this room. We take for granted that the radon diffuses through a $3\rm\ cm$ thick layer of wall.

My attempt

I assume that the activity concentration of the radon is the same as that of the uranium from which it's coming. I compute the activity of the radon using $A = (50\rm\ Bq\,m^{-3})(10^3\ m^3)= 50 000\ Bq$. Then taking one of the four walls, the concentration of uranium is given by the activity per unit volume in the thin layer through which the radon diffuses, that is, $C = (50 000\ \rm Bq)/(10 \times 10 \times 0.03\ m^3)$.

I think this approach is flawed. Any hint towards a more reasonable solution will be appreciated.