Let $\{f_1,\dots,f_m\}$ be an IFs and $E_n$ be the associated self similar set. It's known that $E_n$ is a union of disjoint balls $B(x_i,R\cdot r^n)$ (balls with same radius but not the same center). Find $\dim_HE_n.$
I thought using the fact that it's a union of disjoint balls saying $$\dim_HE_n=\sup\dim_HB_{n,i}$$(where $B_{n,i}$ is the ball which is associated with $f_i$)$$=\dim_HB(x,R\cdot r^n)=Rr^n\dim_HB(0,1)$$From here it seems like the dimension of the unit ball is 1 but I'm not sure since I know nothing about $E_n$ and it can also a non-euclidean space. How can I find the Hausdorff dimension of the unit ball?
EDIT: The original question was 
About part A I said that each ball can be moved in each direction distance of $R\cdot r^n$ "positve and negative" (in the intuition of euclidean space) and thus we would get a bounding with $L(n)$ to the Malinowski dimension. Now I'm stuck at part b. afterwards I'll have to understand how can I solve c.