The $\epsilon$-covering number of the euclidean unit ball in $\mathbb R^d$ scales like $(1/\epsilon)^d$. More formally, >**Lemma.** $(1/\epsilon)^d \le N(\epsilon, B_2) \le (3/\epsilon)^d$. *Proof.* See **Theorem 4.2** and **Example 14.1** of this manuscript http://www.stat.yale.edu/~yw562/teaching/598/lec14.pdf. $\quad\quad\Box$ Now, use this to get (an estimate of) the covering number of $rB_2$, for any $r \ge 0$.