A statistical model is described which empirically relates the volume (characterized by ${\ensuremath{\lambda}}_{i}$) associated with each particle to its mass (${m}_{i}$). The functional dependence used in ${{\mathrm{m}}_{i}}^{\ensuremath{\alpha}}{\ensuremath{\lambda}}_{i}=\mathrm{const}$, where $\ensuremath{\alpha}$ is some constant. The two parameters ${\ensuremath{\lambda}}_{\ensuremath{\pi}}$ and $\ensuremath{\alpha}$, in addition to the masses ${m}_{i}$, determine all the other ${\ensuremath{\lambda}}_{i}$. The model is applied to antiproton-proton annihilation at low and moderate energies. The annihilation is assumed to proceed through all possible intermediate states consisting of all combinations of the five mesons, $\ensuremath{\pi}$, $K$ (or $\overline{K}$), ${K}^{*}$ (or ${\overline{K}}^{*}$), $\ensuremath{\rho}$, and $\ensuremath{\omega}$. The experimental multiplicities and fraction of $K\overline{K}m\ensuremath{\pi}$ ($m=0, 1, 2,\dots{}$) states determine the two parameters ${\ensuremath{\lambda}}_{\ensuremath{\pi}}$ and $\ensuremath{\alpha}$ to be 4.0\ifmmode\pm\else\textpm\fi{}0.4 and 1.94\ifmmode\pm\else\textpm\fi{}0.06, respectively. These values of ${\ensuremath{\lambda}}_{\ensuremath{\pi}}$ and $\ensuremath{\alpha}$ predict the extent to which the ${K}^{*}$ (or ${\overline{K}}^{*}$), $\ensuremath{\rho}$, and $\ensuremath{\omega}$ take part in the annihilation. These predictions are found to be in reasonable agreement with recent experimental data on the role of the ${K}^{*}$ (or ${\overline{K}}^{*}$), $\ensuremath{\rho}$, and $\ensuremath{\omega}$ in $\overline{p}p$ annihilation. The $\ensuremath{\eta}$ meson is also considered.