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In this paper we prove the existence of a maximum for the firstSteklov-Dirichlet eigenvalue in the class of convex sets with a fixed sphericalhole under volume constraint. More precisely, if $\Omega=\Omega_0 \setminus\bar{B}_{R_1}$, where $B_{R_1}$ is the ball centered at the origin with radius$R_1>0$ and $\Omega_0\subset\mathbb{R}^n$, $n\geq 2$, is an open bounded andconvex set such that $B_{R_1}\Subset \Omega_0$, then the firstSteklov-Dirichlet eigenvalue $\sigma_1(\Omega)$ has a maximum when $R_1$ andthe measure of $\Omega$ are fixed. Moreover, if $\Omega_0$ is contained in asuitable ball, we prove that the spherical shell is the maximum.

An isoperimetric inequality for the first Steklov-Dirichlet Laplacian eigenvalue of convex sets with a spherical hole