Solved: Suppose you make napkin rings by drilling holes

Chapter 7, Problem 7.3.42

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Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height , as shown in the figure. (a) Guess which ring has more wood in it. (b) Check your guess: Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius through the center of a sphere of radius and express the answer in terms of .

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