Sensors and methods for producing them are disclosed. A cavity is created and filled with a reagent that includes a conductive matrix, enzyme, catalyst, and binding agent, in a preferred embodiment. The cavity is substantially enclosed, leaving enough of an opening to allow the sample to enter. A portion of the material surrounding the cavity is preferably permeable to a substance useful for measuring reaction, but not to the reagent or the sample. Cavities that have the shape of a cone, conical frustum, pyramidal frustum, and right circular cylinder are given as examples. Other systems include a membrane that contains the sensor's active area and defines an internal volume of fluid, where the membrane or internal volume has a particular geometric relationship to the active area.