Abstract
This article was inspired by a set of 12 cylindrical cups, which are volumetrically indexed; that is to say, the volume of cup n is equal to n times the volume of cup 1. Various sets of volumetrically indexed cylindrical cups are explored. I demonstrate how this children's toy is ripe for mathematical investigation, with connections to geometry, algebra and differential calculus. Students with an understanding of these topics should be able to complete the analysis and related exercises contained herein.
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