The quality of monitoring accomplished by wireless sensor networks (WSNs) mainly depends on the service of coverage provided by the deployed sensors. In particular, redundant coverage is essential to several applications, where an event is simultaneously detected by multiple sensors. While several protocols have been proposed for two-dimensional (2D) space, little work has been focused on three-dimensional (3D) space although it is more accurate for the design of sensing applications. In this paper, we consider the problem of k-coverage in 3D WSNs, where each point is covered by at least k sensors. Specifically, we propose to use Helly's Theorem and the Reuleaux tetrahedron model for characterizing k-coverage of a 3D deployment field. This leads to develop a placement strategy of sensors to fully k-cover a 3D field. Then, we design an energy-efficient sensor selection protocol for 3D k-covered WSNs to extend the network lifetime. We corroborate our analysis with various simulation results.