Suppose you are visiting a factory that produces cheese in a cylindrical shape as shown in Figure 1. You ask the manufacturer to sell you a piece of cheese, similar to the segment in the previous problem, whose volume you raised. The manufacturer agrees to his request, but as there is no scale at hand, he makes a drawing of the cheese and represents it as a rectangle with the cuts by dotted lines indicated in figure 2. By looking at the figure he concludes that the cut you ask (above the red line) is equal to a quarter of the cheese and therefore you must pay a quarter of its total value. a) Do you think that what the manufacturer believes is correct? b) Would you be paying more or would you be paying less for that piece of cheese? c) If it is not a quarter of the cheese, what is the difference between the actual and estimated value? Argue your answer verbally or mathematically. (Hint: You should probably integrate the expression from the previous problem)