Exercise 32

Next, I made a model of the volume from Exercise 32 in Section 12.5 of Stewart’s Essential Calculus. This solid is the region of integration enclosed by the surfaces \(x=0, y=0, y=1-x\), and \(z=1-x^2\).

32_3      32_2

This model is my best by far because the edges are almost perfectly smooth, and each face is very flat. It took about three hours to print, and the only deformities are a little bubble near one edge and the red outline around “\(z=0\)” from of the residual red filament in the extruder. I exported the piece from Mathematica into Cinema 4D, then imprinted the equations into their respective faces (see http://home.wlu.edu/~dennee/math_vis.html for further detail). For this solid I used 300 PlotPoints instead of 100 (see Mathematica code below) and it paid off in the smooth definition of the curved edge, which is almost perfect.


You can find this object on Thingiverse here.

DSC_1140       DSC_1136