(a) At a party, the punch bowl is hemispherical, with 1 foot radius and open at the top. The fruit punch weighs 66 pounds per cubic foot. At the beginning of the party the bowl is full to the brim. The rules for serving punch require each person to fill the ladle, raise it exactly 2 feet above the top of the bowl (without spilling!), and then pour the punch into a cup at that level. After 30 minutes, 40 people have filled 60 cups, and the punch remaining in the bowl is 4 inches deep. Draw a picture of the situation, and then set up the integral for the work W involved - until the punch is only 4 inches deep. Include all pertinent information in the integral, but do not evaluate the integral. (b) Suppose that each person is to raise the ladle exactly 2 feet (not 2 feet above the top of the bowl). Set up the integral for the work W involved until the punch is 4 inches deep. (Does this activity make any sense for the partygoers? Explain why or why not.)