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Ryan Cota
01/31/08 2:29pm

In my calculus class we are doing lots of problems that involve either the washer method or shell method, however visualizing the actual 3d shape generated by rotating around an axis is hard to picture, even if it is not necessary to see the shape to find the volume of it, it would be really helpful to know what the shape looks like.

Here is an example that I have been trying to graph in mathematica version 6 (i.e. I need help with commands from version 6.0)

Problem: y=16-x, y=3x+12, x=-1
now if you plot all of those you get a triangle shape bounded by those 3 equations that is above the x-axis, now I want to rotate the bounded region around the x-axis to create a solid shape and in this case it will have a hole in the middle. Again I know how to find the volume but how do I graph this in 3D. After looking through the MathGroup archive I have tried the following command:

RevolutionPlot3D[{{16 - x, x}, {3 x + 12, x}}, {x, -1, 1},
ViewVertical -> {-1, 0, 0}]

But this is still not correct as not only is the back side not solid but the center cylinder has no depth.



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