. The hoop stress in thin-walled cylinders, subjected to internal pressure, is a fundamental aspect of pressure vessel design. It is calculated by considering the internal pressure (P), the internal diameter (d), and the wall thickness (t) of the cylinder. Among the given options, the correct formula for hoop stress is derived based on these parameters and is given as Pd/2t. This relationship ensures the integrity and safety of cylindrical pressure vessels under operational conditions.