The traffic load of cellular networks varies in both time and spatial domains, causing many base stations (BS) to be under-utilized. Assisted by cell zooming, dynamic BS sleep control is considered as an effective way to improve energy efficiency during low traffic hours. Therefore, how densely the BSs should be deployed with cell zooming and BS sleeping is an important issue. In this paper, we explore the energy-optimal cellular network planning problem with dynamic BS sleeping and cell zooming for the cases in which traffic is uniformly distributed in space but time-varying. To guarantee the quality of multi-class services, an approximation method based on Erlang formula is proposed. Extensive simulations under our predefined scenarios show that about half of energy consumption can be saved through dynamic BS sleeping and power control. Surprisingly, the energy-optimal BS density we obtained is larger than the one without considering BS sleeping. In other words, deploying more BSs may help to save energy if dynamic BS sleeping is executed.