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I have two regions I want to plot, as follows:

  1. The base of the solid $S$ is the triangular region (in the $x$-$y$ plane) with vertices $(0,0)$, $(3,0)$, and $(0,2)$. Cross-sections perpendicular to the $y$-axis are semicircles (assuming upward in the $z$-direction).

  2. The base of the solid $S$ (in the $x$-$y$ plane) is an elliptical region with boundary curve $9x^2+4y^2=36$. Cross-sections perpendicular to the $x$-axis are isosceles right triangles (assuming upward in the $z$-direction) with hypotenuse in the base.

Is there a way in Mathematica to show students what these regions look like?

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This really is more a math question than a Mathematica question. With some amount of thought, one can derive the equations for the requested surfaces:

ContourPlot3D[(x - (3/2 - (3 y)/4))^2 + z^2 == (3/2 - (3 y)/4)^2,
              {x, 0, 3}, {y, 0, 2}, {z, 0, 3/2}, BoxRatios -> Automatic]

surface #1

ContourPlot3D[x^2/4 + (Abs[y] + z)^2/9 == 1, {x, -2, 2}, {y, -3, 3}, {z, 0, 3}, 
              BoxRatios -> Automatic]

surface #2

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  • $\begingroup$ Thanks. The students appreciated viewing this last night. $\endgroup$ – David Jan 27 '17 at 16:35

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