Abstract: Millimeter emission of the quiet Sun is generated entirely in the chromosphere and therefore can serve as a convenient tool for chromospheric plasma diagnostics. This paper presents model calculations of the radio-brightness distribution over the solar disk to test two chosen versions of a modern, realistic, spatially inhomogeneous, three-dimensional model of the chromosphere based on the Bifrost code (Carlsson et al., 2016). Comparison of the calculated and observed data demonstrates agreement: the disk brightness (on average, without small-scale fluctuations reflecting the inhomogeneity of the chromosphere) remains constant up to distances of around 0.95 of the solar radius from the disk center. The model brightness at the limb does not exceed twice the brightness of the disk center, with no significant brightening immediately behind the limb. At the same time, the model values of the radio radius, which characterize the height of the chromosphere, turn out to be much smaller than the observed values available in the literature. This discrepancy (an underestimated value of the radio radius) may be due the fact that a number of physical processes are not taken into account in 3D models, e.g., the LTE assumption (Martínez-Sykora et al., 2020). Conversely, the observed values of the radio radius may be overestimated, as evidenced by our recent eclipse measurements in 2020.