Let $\Gamma$ be a discrete subgroup of the isometry group of $\mathbb R^n$ and $O=\mathbb R^n/\Gamma$ is the orbifold.

If there exists a point $p \in O$ such that $$ \lim_{r \to \infty}\frac{\text{Vol} B(p,r)}{r^n} >0, $$ can we prove that $\Gamma$ must be finite?