You are working in a factory that uses water in its cooling systems and consequently has a lot of steam reservoirs. Due to carclessness, a \(70.0-\mathrm{kg}\) metal plate has been left on top of the only steam vent for a certain steam reservoir, and as a result the pressure in the reservoir builds up sufficiently to lift the plate a small distance. With the plate raised, the reservoir pressure drops slightly, and the plate lowers slowly back down and gently comes to rest on top of the vent. The vent is circular and has a diameter of \(100 \mathrm{~mm}\), and the plate is a square, \(450 \mathrm{~mm}\) on a side. No steam is seen seeping out after this incident, and so you assume the plate has made a good seal such that only the circular section of plate directly above the vent is in contact with the steam. A flow meter attached to the reservoir tells you that \(108 \mathrm{~kg}\) of liquid water was piped into that reservoir, and you know that this reservoir has a volume of \(100 \mathrm{~m}^{3}\). A coworker sees a few drops of water that have condensed on a glass portal located in the reservoir wall and thinks that the steam in the reservoir must have cooled enough to begin condensing to water (most of what's in the reservoir is still steam, though). Your coworker is about to grab the plate with his hands in order to uncover the vent and allow the steam to escape as it is designed to do when you suddenly realize that touching the plate might not be a good idea.