This paper investigates the performance of cooperative spectrum sensing in cognitive radio networks using the stochastic geometry tools. In order to cope with the diversity of received signal-to-noise ratios at secondary users, a practical and efficient cooperative spectrum sensing model is proposed and investigated based on the generalized likelihood ratio test detector. In order to investigate the cooperative spectrum sensing system, the theoretical expressions of the probabilities of false alarm and detection of the local decision are derived. The optimal number of cooperating secondary users is then investigated to achieve the minimum total error rate of the final decision by assuming that the secondary users follow a homogeneous Poisson point process. Moreover, the theoretical expressions for the achievable ergodic capacity and throughput of the secondary network are derived. Furthermore, the technique of determining an appropriate number of cooperating secondary users is proposed in order to maximize the achievable ergodic capacity and throughput of the secondary network based on a target total error rate requirement. The analytical and simulation results validate the chosen optimal number of collaborating secondary users in terms of spectrum sensing, achievable ergodic capacity, and throughput of the secondary network.