Problem 2. Consider a circular disc with a sector of angle 0 removed. Imagine rolling this shape into a conical cup, like one often nds at water coolers. a. Show that if this is rolled into a cone the top of the cone will have radius 1 i and 271' I 0 ' _ _ _ 2 he1ght 1 (1 27r) . Hint: If we remove a sector of angle 0 what is the circumference of the remaining piece? b. How should one choose 0 to maximize the volume of the cup? Recall that the vol- ume of a right cone is bh. You might find it easier to work with the quantity 0 = 1 . y 23