The figure below shows a simplified schematic of a float valve used to control the water level in a tank. A float is connected by a cable to a heavy stopper covering a hole at the bottom of the tank. When the level of water in the tank goes above the maximum allowed, the stopper moves up and lets some water leave through the hole at the bottom until the level goes back down to the limit level. Float Water Stopper For the system in the figure, the stopper has the shape of a truncated cone with a thickness of 5 mm. The top and bottom of the stopper have diameters of 50 mm and 40 mm, respectively, and the stopper is made of steel with a density of 7.85 g/cm. The bottom of the tank is exposed to the atmosphere. (a) (11 pts) If the cable has a length of 1.5 m and the diameter of the float is 65 cm, what is the maximum possible level of water in the tank? What fraction of the height of the float is above the water when that level is reached? You may assume that the density of water is 1 g/cm', and that the weight of the float and the cable are negligible compared to the weight of the stopper. (b) (12 pts) For the system in part (a), you wish to adjust the maximum possible level by using floaters with different diameters. If everything else stays the same, what are the minimum and maximum possible values of the maximum level that can be set by changing the diameter of the floater only?