Part 1 A rectangular tank with a square bottom has base side lengths of 3 feet and a height of 10 feet is filled with 6 feet of water. The tank is designed for the water to drain keeping the integrity of the shape of the tank and the side lengths will change at a rate of feet per second once it is drained. How fast would water drain? Part 2 The water needs to drain into a cylindrical container. Find the minimum amount of material needed to construct the container. Part 3 Once the container is fully filled with water a pump 2 feet below the container will activate. Find how much work is required to pump the water from container. Part 4 The water is to be pumped into a vase that is created by the equation x = 3 sin + 15 being rotated about the y-axis. The vase stands 40 inches tall. How much water the vase hold? (There are 1728 cubic inches in a cubic foot) Final Question How many vases are needed to collect all the water?