We study elastic scattering of ultracold atoms by a conducting sphere. Loss of flux through inelastic reactions and adsorption is described in an unambiguous and model-independent way by incoming boundary conditions in the semiclassical region near the surface of the sphere. Differential cross sections are presented for Na and metastable $\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)$ atoms scattered by a nanosphere with radius $200\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ or $2000\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ Their near-threshold behavior is determined by a small number of parameters which are properties of the potential tail beyond the semiclassical regime, and it depends sensitively on the characterstic lengths ${\ensuremath{\beta}}_{6}$, ${\ensuremath{\beta}}_{7}$ which describe the strength of the nonretarded van der Waals part and the highly retarded Casimir part of the atom-sphere interaction, respectively. These lengths can be tuned to probe various regions of the atom-sphere interaction by appropriate choice of the radius of the sphere.