3D Plotting with 2 functions with single variable

Question

I was given an assignment which is to plot the same shape as the one in the link. https://i.stack.imgur.com/PAHMO.png

The shape is comprised of 2 functions: $z = 1 - y$ (1), $y = \sqrt{x}$ (2) and $z = 0$. I tried using Mathematica for the first time and got a successful result with function (1), but function (2) doesn't seem to work as I expected. I tried the command

 Plot3D[y == Sqrt[x] , {x, 0, 1}, {y, 0, 1}, AxesLabel -> {x, y, z}, AxesOrigin -> {0, 0, 0}, Boxed -> False]

and received: I know it doesn't make sense at all, since I think the program only plots $z=f(x,y)$ correctly, not $y = f(x)$ or even $y=f(x,z)$. Somehow online tools such as https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/ got this worked out perfectly.

Right now I'm stuck and I have been trying my best to find a solution. I post the problem here and hopefully I can receive all the help available.

Answer 1

You need to use RegionPlot3D

Clear[x, y, z]
RegionPlot3D[{x < 1 && y < 1 && z < 1 && z < 1 - y && 
   y > (x)^(1/2)}, {x, 0, 1.1}, {y, 0, 1.3}, {z, 0, 1.1}, 
 PlotStyle -> {Blue, Opacity[0.4]}, Mesh -> None, 
 AxesLabel -> Automatic, PlotPoints -> 200]

Answer 2

Use ContourPlot3D or ParametricPlot3D to Plot y == Sqrt[x].

ContourPlot3D[y == Sqrt[x], {x, 0, 1.2}, {y, 0, 1.2}, {z, 0, 1.2}, ViewPoint -> {3.2, -0.13, 1.0}]

Or

ParametricPlot3D[{x, y, z} /. y -> Sqrt[x], {x, 0, 1.2}, {z, 0, 1.2}, 
 ViewPoint -> {3.2, -0.13, 1.0}]

Besides RegionPlot3D, we can also use RegionFunction to cut the surfaces and then Show the elements.

Here is an attempt.

SetOptions[ContourPlot3D, RegionBoundaryStyle -> None, 
  AxesLabel -> {x, y, z}, ViewPoint -> {3.02, 0.64, 1.30}, 
  Mesh -> None, Boxed -> False, Axes -> False];
surf1 = ContourPlot3D[
   y == Sqrt[x], {x, 0, 1.2}, {y, 0, 1.2}, {z, 0, 1.2}, 
   RegionFunction -> Function[{x, y, z}, z <= 1 - y], 
   ContourStyle -> Red];
surf2 = ContourPlot3D[
   z == 1 - y, {x, 0, 1.2}, {y, 0, 1.2}, {z, 0, 1.2}, 
   RegionFunction -> Function[{x, y, z}, y >= Sqrt[x]], 
   ContourStyle -> Green];
surf3 = ContourPlot3D[z == 0, {x, 0, 1.2}, {y, 0, 1.2}, {z, 0, 1.2}, 
   RegionFunction -> Function[{x, y, z}, y >= Sqrt[x] && z <= 1 - y ],
    ContourStyle -> Blue];
surf4 = ContourPlot3D[x == 0, {x, 0, 1.2}, {y, 0, 1.2}, {z, 0, 1.2}, 
   RegionFunction -> Function[{x, y, z}, z <= 1 - y ], 
   ContourStyle -> Yellow];
axes = Graphics3D[{Arrow@*
      Tube /@ {{{0, 0, 0}, {1.2, 0, 0}}, {{0, 0, 0}, {0, 1.2, 
        0}}, {{0, 0, 0}, {0, 0, 1.2}}}}];
Show[surf1, surf2, surf3, surf4, axes]