  The unit ball random geometric graph $G=G^d_p(\lambda,n)$ has as its vertices
$n$ points distributed independently and uniformly in the $d$-dimensional unit
ball, with two vertices adjacent if and only if their $l_p$-distance is at most
$\lambda$. Like its cousin the Erdos-Renyi random graph, $G$ has a connectivity
threshold: an asymptotic value for $\lambda$ in terms of $n$, above which $G$
is connected and below which $G$ is disconnected (and in fact has isolated
vertices in most cases). In the connected zone, we determine upper and lower
bounds for the graph diameter of $G$. Specifically, almost always,
$\diam_p(\mathbf{B})(1-o(1))/\lambda \leq \diam(G) \leq
\diam_p(\mathbf{B})(1+O((\ln \ln n/\ln n)^{1/d}))/\lambda$, where
$\diam_p(\mathbf{B})$ is the $\ell_p$-diameter of the unit ball $\mathbf{B}$.
We employ a combination of methods from probabilistic combinatorics and
stochastic geometry.
