Context. The Sun is an extraordinary workbench, on which several fundamental astronomical parameters can be measured with high precision. Among these parameters, the solar radius R ⊙ plays an important role in several aspects, for instance, in evolutionary models. Moreover, it conveys information about the structure of the different layers that compose the solar interior and its atmosphere. Despite the efforts to obtain accurate measurements of R ⊙ , the subject is still debated, and measurements are puzzling and/or lacking in many frequency ranges. Aims. We determine the mean, equatorial, and polar radii of the Sun ( R c , R eq , and R pol ) in the frequency range 18.1 − 26.1 GHz. We employed single-dish observations from the newly appointed Medicina Gavril Grueff Radio Telescope and the Sardinia Radio Telescope (SRT) in five years, from 2018 to mid-2023, in the framework of the SunDish project for solar monitoring. Methods. Two methods for calculating the radius at radio frequencies were employed and compared: the half-power, and the inflection point. To assess the quality of our radius determinations, we also analysed the possible degrading effects of the antenna beam pattern on our solar maps using two 2D models (ECB and 2GECB). We carried out a correlation analysis with the evolution of the solar cycle by calculating Pearson’s correlation coefficient ρ in the 13-month running means. Results. We obtained several values for the solar radius, ranging between 959 and 994 arcsec, and ρ , with typical errors of a few arcseconds. These values constrain the correlation between the solar radius and solar activity, and they allow us to estimate the level of solar prolatness in the centimeter frequency range. Conclusions. Our R ⊙ measurements are consistent with the values reported in the literature, and they provide refined estimates in the centimeter range. The results suggest a weak prolateness of the solar limb ( R eq > R pol ), although R eq and R pol are statistically compatible within 3 σ errors. The correlation analysis using the solar images from the Grueff Radio Telescope shows (1) a positive correlation between solar activity and the temporal variation in R c (and R eq ) at all observing frequencies, and (2) a weak anti-correlation between the temporal variation of R pol and solar activity at 25.8 GHz.