How does one go about finding the volume of an irregular shape? Students get a preview of integral calculus as they compute volume of a solid as the sum of volumes of slices of the solid. Extensions of the problem and a complete discussion of the underlying mathematical ideas is included. This mathematically rich problem was originally developed for the Project Discovery Mathematics by Inquiry institutes for middle grades teachers taught in 1992 - 1994 at Ohio State University. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)