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Though beaconless geographic routing protocols get rid of the overhead caused by the periodic beacon messages to be broadcast in case of beacon based approaches. But, most of the existing beaconless routing protocols do not consider remaining energy of nodes while making routing decisions. This may result in the repetitive selection of a particular node which is at shortest distance from destination, among its neighbors. This will result in its battery power to drain out faster causing a possible hole in the network. Also most of the existing geographic routing algorithms assume a two-dimensional topology. But, some real world applications demand a Wireless Sensor Network (WSN) to operate in three dimensional space. This paper proposes an energy aware beaconless geographic routing approach for three dimensional WSNs. It takes into account energy budget of nodes besides the distance, in next hop forwarder selection process. This increases the life -time of the network by maximizing the lifetime of the nodes. The simulation results also validate the proposed approach and are being presented in this paper.