By "disk" I mean the set of points inside a circle in 2D euclidean space.
This may seem like an absurd question, because Im pretty sure the answer is 2, but I just cannot see how to prove it.

As far as I understand from the topological definition of a Hausdorff measure, you need to find an optimal covering of your set with a given maximal diameter. But I also remember that the cover of a unit circle by smaller circles is not a generally solved problem. (there was this pie-eating game online that i cannot find about this)

It occured to me that I cannot construct a limit easily from which I can get the Hausdorff exponent.

Is this an easy job and Im missing something or is this unsolved?

Maybe a series of maximal diameters exist that goes to 0 and allow for simple optimal covers? Would this be a sufficient condition?

Thanks, this is pretty far from my job, it just bothers me.