(4) A tank in the shape of an inverted right circular cone (pointy end down) has height 5 feet and radius 4 feet. The tank is partially filled with 3 feet of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank, assuming the density of the hot chocolate is 1070 pounds per cubic foot, using the slice-approximate- integrate strategy. (5) Suppose that a cylindrical water tank with a hole in the bottom is filled with water. The water, of course, will leak out and the height of the water will decrease. A physical principle called Torricelli's Law implies that the height decreases at a rate proportional to the square root of the height. (a) Set up a differential equation that describes Torricelli's Law. Be sure to clearly explain what each variable represents. (b) Suppose that the water is 170 feet high at midnight, and 135 feet high at noon (the same day, 12 hours later). Find an expression for the height of the water as a function of time