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Recent advances in computing technology have led to the production of a new class of computing device: the wireless, battery powered, smart sensor. A Wireless Sensor Network (WSN) is an ad-hoc network composed of densely-populated tiny electronic sensing devices, distributed over an area or volume. Deployment of a sensor network can be in a random fashion or can be planted manually. These networks promise a maintenance free, fault-tolerant platform for gathering different kinds of data. In this paper, contrary to existing techniques, the deployment problem in a three dimensional space is rigorously analyzed. The problem of determining the minimum number of sensor nodes that guarantee complete coverage is studied which will serve as an optimality measure for the coverage problem.