  In this note we examine the volume of the convex hull of two congruent copies
of a convex body in Euclidean $n$-space, under some subsets of the isometry
group of the space. We prove inequalities for this volume if the two bodies are
translates, or reflected copies of each other about a common point or a
hyperplane containing it. In particular, we give a proof of a related
conjecture of Rogers and Shephard.
