Mathematics is both a key to unlocking the secrets of nature and, for many students, a stumbling block to conceptual understanding in science. In this activity, two sheets of 8.5 in. × 11 in. paper are used to construct two cylinders with surprisingly different volumes (as related to the diameter differences between the unmentioned, missing bases). Extensions include the empirical discovery of pi and a volume illusion with two cone-shaped glasses. These activities feature the mathematical formula for the volume of a cylinder, the importance of quantitative measurements versus simple “eyeball” estimates, and the advantages of measuring in metric versus English units.