Related Rates Lab Preparation 1. Wheat is poured through a chute at the rate of 20 cubic feet per minute, = 20, in a conical pile whose bottom radius is always half the height. Leave all answers in exact form (in terms of 7). Recall that the volume of a cone is given by the formula V = $Tr2h. (a) Sketch a diagram to organize the given information. (b) Using the fact that the bottom radius, r, is always half the height, write the volume of the conical pile as a function of radius alone, then find dy (c) Using the result from part (b), at what rate is the bottom radius of the wheat pile changing, of =?, the moment when the radius reaches a measure of 3 feet, r = 3? (d) Using the fact that the bottom radius, r, is always half the height, write the volume of the conical pile as a function of height alone, then find dy (e) Using the result from part (d), what is the height of the conical pile, h =?, when the height of the pile is increasing at a rate of 4 ft/min, at ah = 4. (f) Given V = mr2h. Find dy in terms of r, h, dr, and an. (g) Use this equation for from (f) to answer (i) and (ii) below: i. We know that h = 2r, thus dh = 2 . dr. Plug these into the equation for du and confirm your result in part (b). ii. We know that r = th, thus of = 5 . 92. Plug these into the equation for dy a confirm your result in part (d)