Related Rates Problems
Math 1100
23 October, 2013
Steps to Solve Optimization Problems
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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?
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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 .)
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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?
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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.)
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