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Minimization of uncovered area fraction subject to a power constraint and minimization of power requirement subject to an upper limit for uncovered area fraction are considered for large-scale wireless sensor networks. Analysis shows that deploying sensors with homogeneous sensing ranges is optimal with respect to the formulated optimization problems. As such, deployment of multi-tier hierarchical networks of sensors with differing sensing capabilities may not improve coverage when a network-wide power constraint is present. In addition, heterogeneity does not help in reducing network-wide power requirement when there is a coverage constraint.