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In this paper, the backscattered electric field is derived when a plane electromagnetic wave is incident upon a perfectly conducting sphere coated with a radially inhomogeneous dielectric. The Mie series is obtained and then subjected to an asymptotic analysis that is valid for very short wave-lengths. In particular, the first two terms for the reflected portion of the electric field are derived and the formulation for the creeping wave contribution is presented. Also, a numerical computation of the monostatic cross section is performed for various thicknesses of the coating by considering the reflected portion of the backscattered electric field. It is shown that this particular type of inhomogeneous sheath reduces considerably the monostatic cross section of the perfectly conducting sphere as its thickness increases.