A spherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute. (a) Find the rates of change of the radius when r = 30 centimeters and r = 95 centimeters. r = 30 cm/min X r = 95 cm/min X At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 12 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate (in ft/min) is the height of the pile changing when the pile is 12 feet high? (Hint: The formula for the volume of a cone is V = m'zh.) db = _ ft min dt / An airplane is flying in still air with an airspeed of 300 miles per hour. The plane is climbing at an angle of 26. Find the rate at which the plane is gaining altitude. (Round your answer to four decimal places.) E m r