Consider a symmetric convex body $A$ in $\mathbb{R}^d$. Now, we draw another object, $A'$, concentric and translated with respect to $A$ and having radius slightly greater than twice to the radius of $A$. (By this I mean the centers of $A$ and $A′$ are the same, and $A′$ is $2+\epsilon$ times scaled to $A$ but without rotation.)

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

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