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Calculus 12 - Applications Assignment Related Rate and Optimization Name: Complete the following questions showing all required work 1 Sand is being poured into a conical pile in such a way that the height is always twice the radius of the base. The volume is increasing at 30 m/min. Find the rate at which the radius is increasing at the instant the height is 6m. 2. A cylindrical beaker of radius 10 cm is being drained at a rate of 25 cm/min. Find the rate at which the depth of the liquid is decreasing, when the depth is 2 cm. (Hint: If the liquid is draining should the rate be negative or positive)

3. Two cars leave an intersection at the same time. One car is heading west at 80 km/hr and the other south at 100 km/hr. Assuming no changes in direction or velocity, at what rate are the cars separating half an hour later?