This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Analysis Model Tutorial A child loves to watch as you fill a transparent plastic bottle with shampoo (figure below). Every horizontal cross section of the bottle is circular, but the diameters of the circles have different values. You pour the brightly colored shampoo into the bottle at a constant rate of 15.4 cm/s. At what rate is the level in the bottle rising at the following? d2- (a) a point where the diameter of the bottle is di = 6.50 cm (b) a point where the diameter is d = 1.33 cm Part 1 of 5-Conceptualize: The volume flow rate of shampoo into the bottle is constant. Let us imagine a given volume of shampoo having the shape of a disk whose volume is the product of a circular cross section of the bottle and the vertical thickness of the disk. The rate at which the level of shampoo in the bottle is rising is the same as the rate at which the vertical thickness of the disk is Increasing. Because the volume is increasing at a constant rate, the level of shampoo will be increasing rapidly where the cross section of the bottle is small; the level will be increasing slowly where the cross section is large. A.CA DM