Computational modeling of so-called active surfaces is a new research field with many interesting applications in biology. It requires solving time-dependent partial differential equations on evolving surfaces and domains, and many state-of-the-art finite element methods face challenges regarding the meshing of these geometries. Therefore, we want to use cut finite element methods that allow the geometry to cut arbitrarily through a fixed background mesh, to simplify the discretization of the geometry. To be able to carry out these large, coupled problems in 3D, it is crucial to access good computational resources.