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The rapid development of wireless technologies and embedded sensing devices has made it possible for people to monitor, control and interact with the physical world via wireless sensor networks. While holding promise in a wide variety of applications, sensor networks are driven by extremely limited energy resources. This necessitates the energy aware design and operation of the sensor network. One of the fundamental issues in sensor networks is the coverage problem. In this paper, contrary to existing techniques, the coverage problem in a three dimensional space is rigorously analyzed. Given a distribution of sensor nodes, a new distributed algorithm to choose a subset of working nodes for full coverage is derived. A computationally efficient algorithm to check for complete coverage is also proposed