  Let $O$ be a closed $n$-dimensional arithmetic (real or complex) hyperbolic
orbifold. We show that the diameter of $O$ is bounded above by $$\frac{c_1\log
vol(O) + c_2}{h(O)},$$ where $h(O)$ is the Cheeger constant of $O$, $vol(O)$ is
its volume, and constants $c_1$, $c_2$ depend only on $n$.
