Numerical and analytic solutions in the ray-optics region have been obtained for the scattering of HF radio waves by a spherical electron cloud with a Gaussian distribution of electron density in the radial direction. The results show that a highly overdense or hard cloud has a wide range of backscatter angles for which the cross section is almost constant with a value close to that of an equivalent conducting sphere (critical radius size). A slightly overdense or soft sphere has a much narrower range of almost constant cross section whose value is proportional to the fourth power of the critical radius and considerably below that of an equivalent conducting sphere. In the region of forward scatter, all spheres have essentially the same cross section, independent of hardness. For underdense spheres, the cross section is generally the same as that characteristic of forward scattering except in the region of maximum deflection where the cross section increases very sharply. It is found that when an underdense sphere becomes critical, the maximum deflection is 90°, whereas an overdense sphere retains its maximum deflection of 180° at the critical density. For overdense spheres, the analytic results are in good agreement with those obtained numerically; but for underdense spheres, they are not in good agreement at the higher electron densities.