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Backscattering is calculated for an acoustic wave incident on a hard or soft finite cone, and for an electromagnetic wave incident on a perfectly-conducting finite cone. Two shapes of cone are treated, one with a flat base and the other with a rounded base. The calculation is based on the geometrical theory of diffraction. It is probably valid for wavelengths as large as the cone dimensions or smaller. Graphs of the backscattering cross section vs cone angle and vs wavelength are given for axial incidence on the flat-based cone. Suggestions for shaping an object to minimize its backscattering are also included.