This is a poster project whereby students create 3-dimensional models of physical objects by using cross sections. Students determine what functions to use for their base regions and the cross sections. They use a spreadsheet to calculate the Riemann sum for their objects and compare their calculations to their integral values. Students have a lot of fun with this project and they get very creative. I recommend that you allow at least 3 weeks for the project and require them to submit their spreadsheets about 1 week into the project. As an instructor, you'll want to make sure that you are very comfortable with the math required and with formulas in Excel. The zip file contains a sample Excel spreadsheet for a project, a detailed project description and specifications for the students, project evaluation forms that students fill out for each other and for themselves, and a project scoring sheet. Files are in both MS Word (or MS Excel) and pdf formats. Also included is winplot.exe, a free software program that allows students to see a 3-D image of their project (and print it) before they build it.
NOTE: Students should modify the spreadsheet to reflect either a right Riemann sum or left Riemann sum by summing one less row (slice). The sample spreadsheet does not do this since the first and last rows (slices) have a zero volume and it would not change the Riemann sum calculation.