 Busemann–Petty problem

The Busemann–Petty problem is a classic question in the field of convex geometry. It asks whether, in Euclidean space, the volume of a convex body can be deduced solely from the volumes of its orthogonal projections onto a hyperplane. More specifically, if two convex bodies have the same volume for all orthogonal projections, do they necessarily have to be congruent (that is, identical up to rigid motion)?