Electron energy loss spectroscopy in a high-resolution transmission electron microscope has recently been used with success to characterize the electronic properties of closed cage nanometer-size graphitic particles. In the plasmon region, the experimental data reveal interesting size-dependent variations, which are not yet fully understood. The difficulties encountered in the interpretation of the spectra are principally due to the lack of a complete theoretical treatment of the anisotropic dielectric response in nanometer-size particles. In order to obtain a better understanding of the experimental data we propose a model based on nonrelativistic local dielectric response theory for electrons penetrating through a nested concentric-shell fullerene or the so-called "carbon onion." The anisotropy of the electronic properties of the sphere is taken into account via the frequency-dependent dielectric tensor of graphite. The model can be applied to simulate electron energy loss spectra as well as line scans through energy filtered images and allows thus a direct comparison to experimental data.