One of the major concerns in wireless sensor networks is improving the network lifetime. In this paper, we propose an event reporting scheme and we show that based on it the average amount of energy required to report an event to the sink decreases when the network sensor density increases. Moreover, we prove that the speed of increasing the network lifetime goes up faster than that of the network density. Based on this result, we derive the minimal number of sensor nodes required to supervise a given area during a given period. Finally, we prove that these nodes must be deployed at the same time and not over different deployment phases.