Shoreline Community College Complementary Coffee Cups Calculus Problem Project Choice 1: COMPLEMENTARY COFFEE CUPS (Textbook Pg. 568)
Suppose you have a choice of two coffee cups of the type shown, one that bends outward and one
inward, and you notice that they have the same height and their shapes fit together snugly. You wonder
which cup holds more coffee. Of course, you could fill one cup with water and pour it into the other one
but, being a calculus student, you decide on a more mathematical approach. Ignoring the handles, you
observe that both cups are surfaces of revolution, so you can think of the coffee as a volume of
revolution.
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