Students sometimes struggle with visualizing the three-dimensional solids encountered in certain integral problems in a calculus class. We present a project in which students create solids of revolution with clay on a pottery wheel and estimate the volumes of these objects using Riemann sums. In addition to giving students an opportunity for tactile learning, this project focuses students' attention on concepts relating to (i) functions that have no algebraic formula; (ii) notation and construction of Riemann sums; and (iii) error estimation. We will describe our project design, implementation, and suggested adaptations.