This study presents the results of a series of design experiments that aimed to engage twelve fourth-grade students in mathematical activity exploring the volume of right prisms and cylinders as a dynamic sweep of a surface through a height, an approach that is referred to as Dynamic Measurement for Volume (DYME-V). This article describes this approach and discusses the qualitatively different forms of DYME-V reasoning that students exhibited through this mathematical activity. The analysis of students' reasoning illustrates how students may reason about the quantities involved in DYME-V, their multiplicative relationship, and also their coordinated multiplicative change. The findings show the potential of the DYME-V approach for supporting a perception of right prisms and cylinders as spaces that are generated and thus defined by other objects as the approach emphasizes dynamic images of change in volume measurement.