Volume: 16 cylindrical shells

thingiverse

The region bounded by the function y = 2x^2 - x^3 and the x-axis is rotated about the y-axis generating a volume of revolution. This model displays this volume approximated by sixteen cylindrical shells. (The sixteenth shell in the center contributes no volume, so it is excluded from the print model!) Note that this volume of revolution is an instance where its volume cannot be determined using the disk method. This object was created and printed by my WLU summer research student Ryan McDonnell ('17). Detailed information on how to design it can be found at http://mathvis.academic.wlu.edu/2015/06/24/volume-by-cylindrical-shells/ Instructions This model was manufactured using a MakerBot2X. The recommended printing settings are: Two shells 0.20mm layer thickness 10% infill with a hexagonal pattern No supports required Rafting is recommended The first time this object was printed, it was created without a raft and was extremely challenging to remove from the build bed. We strongly suggest printing with a raft for easier removal of the object.