Radiation of charged particles moving in the presence of dielectric targets is of essential importance for various applications in accelerator and beam physics. As a rule, the sizes of these targets are much larger than the wavelengths under consideration. This fact gives an obvious small parameter of the problem and allows developing approximate methods for analysis. Here we apply one such method (called the “aperture method” in our preceding papers) to analysis of Cherenkov radiation from a charge flying through a vacuum channel in a dielectric sphere. We present analytical results and describe the main physical effects. Typical angular and radial distributions of the radiation field are also presented. In particular, it is shown that the field has an expressed maximum at a certain distance from the sphere. Special attention is paid to the far-field area where the radiation is formed, and corresponding angular distribution does not depend on the distance from the sphere.