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Related Rates Problems Math 1100 23 October, 2013 Steps to Solve Optimization Problems 1. Step 1 2. Step 2 3. Step 3 4. Step 4 5. Step 5 1. Two humans are fleeing from a zombie. Alice is riding her bicycle north at 24 miles per hour and Bruce is running east at 7 miles per hour, starting from the same point. How fast is the distance between Alice and Bruce increasing after two hours? Page 2 2. A spherical balloon is being inflated at the rate of 5 in3 /min. At what rate is the radius increasing when the radius of the balloon is 5 inches? (You may wish to use one of these formulas: V = 34 πr3 and A = 4πr2 .) Page 3 3. The side length of a cube is increasing at the rate of 2 cm/s. How fast is the surface area of the cube increasing when the length of each side is 8 cm? Page 4 4. Water fills a conical cup of radius 2 cm and height 8 cm in deep at the rate of 6 cm3 /min. How fast is the depth of the water changing when it is 5 cm deep? (Recall the the volume of a cone is given by V = 31 πr2 h.) Page 5