Suppose You Make Napkin Rings by Drilling Holes with Different $t$

question 36

Multiple Choice

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 h as shown in the figure. Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius d through the center of a sphere of radius D and express the answer in terms of $t$ .

• A) \(V=\frac{1}{3} \pi t^{3}\)
• B) \(V=\frac{1}{4} \pi t^{3}\)
• C) \(V=\frac{1}{3} \pi t^{2}\)
• D) \(V=\frac{1}{6} \pi t^{2}\)
• E) \(V=\frac{1}{6} \pi t^{3}\)

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