We demonstrate a microfluidic device capable of tracking the volume of individual cells by integrating an on-chip volume sensor with pressure-activated cell trapping capabilities. The device creates a dynamic trap by operating in feedback; a cell is periodically redirected back and forth through a microfluidic volume sensor (Coulter principle). Sieve valves are positioned on both ends of the sensing channel, creating a physical barrier which enables media to be quickly exchanged while keeping a cell firmly in place. The volume of individual Saccharomyces cerevisiae cells was tracked over entire growth cycles, and the ability to quickly exchange media was demonstrated.