Bose-Einstein condensates of 10 4 8 5 Rb atoms in a cylindrical trap are studied using a recently proposed approach based on a local-density approximation. Since the existence of a Feshbach resonance allows for widely tuning the scattering length of the atoms, values of the peak gas parameter x p k of the order of 10 - 2 may be attained and the standard analysis based on Gross-Pitaevskii and/or Thomas-Fermi equations may result in being questionable. Energy functionals derived from the correlated basis functions theory and the low-density expansion for a homogeneous hard-spheres gas are used to estimate corrections to the Gross-Pitaevskii equation. The two functionals give similar results, both showing large differences with respect to the Thomas-Fermi and Gross-Pitaevskii ones. The column densities at z=0 may differ by as much as ∼30% and the half maximum radius by ∼20%. The scattering lengths estimated by fitting the half maximum radius may differ by ∼40% from those given by a Thomas-Fermi-based analysis of the experimental data.