Related Rates (#differentiation) Solve the following problems using rates method. (Adapted from Stewart) (a) A spherical iron ball 6 cm in diameter is coated with a layer of ice with uniform thickness. If the ice melts at a rate of 25 cm³/min how fast is the thickness of the ice decreasing when it is 4 cm thick? 4

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 is the height of the pile changing when the pile is 2 feet high? (Hint: The formula for the volume of a cone is V = {mr?h.)

1A) What are the units of the rate of change of f(t) with respect of t?        What does this rate mesuare?

4. Please help me answer this question we’ll calculate and explained. A stone is thrown from the top of a 200 m cliff. The height of the stone relative to the ground is represented by the formula (shown in the image). The time t is in seconds and the height h in meters. A) Calculates its initial speed (instant variation rate at 0s.). B) Calculates the average rate of change for the first two seconds. C) Calculates the rate of instantaneous change at 2 seconds. D) From the results obtained in a), b) and c), describe the displacement of the stone.