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.