We consider a many-to-one sensor network in which a large number of sensors are deployed to monitor an environment. We study sensor activity management therein to maximize the network lifetime while meeting the network resolution requirement. Specifically, in each transmission round the sink estimates the number of active sensors and broadcasts control information to the sensors for activity management. We first consider the case with accurate estimation, and devise a sensor activity control scheme under which the number of active sensors would converge to the minimum one that can meet the requirement. Next, we study the case when the estimation is inaccurate, and propose a stochastic approximation method to minimize the average number of active sensors.