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Applications of the Derivative 1) At a certain instant when the circumference of a circle is 12?: meters, the circumference of that n circle is increasing at a rate of 5 meters per hour. At what rate is the area of this circle increasing at this instant? 2) A person who is 5 ft tail is walking away from a lamppost at a rate of 30 ft per minute. At the moment that they are 10 ft away, their shadow is 20 ft long. Find the rate at which the length of the shadow changes when the person is 30 ft from the lamppost. 3) | -4 hft A cylindrical barrel with a diameter of 2 it collects rainwater, as shown in the gure above. The water drains out through a valve (not shown) at the bottom of the barrel. The rate of change of the dh height. h, ofthe water in the barrel with respect to time is modeled by E = E h, where h is measured in ft and t is measured in seconds. (The volume of a cylinder is V = nrzh) Find the rate of change of the Volume of the water with respect to time when the height of the height of the water is 6 ft. Indicate unit of measure