So, I'm pretty noobish when it comes to physics or math, but this thing came into my head.

We have our ideal gas equation: $PV=nRT$. So under constant temperature and amount of particles $PV=k$. So $P \sim 1/V$. What else is directly proportional to $P$?

Well, one over the surface area of the container: $P \sim 1/A$. So $P \sim 1/V \sim 1/A$. So the area of the container is then directly proportional to the volume of the container $A \sim V$. So this is probably generally not the case, but even for a sphere we can see that this is not the case, as the constant of proportionality chances with the radius: $V = r/3 \* A$, for a given radius $r$.

Given that all this makes sense, what I'm wondering is: How can $P \sim 1/V$?