Consider a symmetric convex body $A$ in $R^d$. Now, we draw another object, $A'$, concentric and translated  with respect to A and having radius slightly greater than twice to the radius of $A$. 

Now my question is that  how many translated copies (upper and lower bound) of $A$ would be required to cover annulus obtained between $A$ and $A'$?


Please let me know if I am not able to put the question clearly.