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I am not really familiar with Mathematica. I wonder if some one can help me draw any of the following surfaces. I will be appreciative if you tell me how to use equations and PlotRange to draw those.

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Welcome to Mathematica.SE. Where do these images come from? Do you want to draw these three specific shapes or are they merely examples? –  Mr.Wizard Sep 17 '13 at 1:23
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A good starting point will be this and that. –  Sektor Sep 17 '13 at 1:39
    
I wanted to draw those and I kind of got the first two but about the last one I am not sure . –  Maggie Sep 19 '13 at 0:01
    
First one: RegionPlot3D[ Sqrt[x^2 + y^2] <= z && x^2 + y^2 + z^2 <= 2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Mesh -> None, AxesLabel -> {x, y, z}, PlotRange -> All, PlotPoints -> 120, PlotStyle -> Directive[Yellow, Specularity[White, 20], Opacity[0.5]]] –  Maggie Sep 19 '13 at 0:01
    
Second one: Show[Graphics3D[{Yellow, Sphere[{0, 0, 0}, 1], Red, Sphere[{0, 0, 2}, 1], Blue, Sphere[{0, 0, -2}, 1]}, Axes -> True, AxesLabel -> {x, y, z}] , ContourPlot3D[x^2 + y^2 == 1, {x, -5, 5}, {y, 0, 5}, {z, -5, 5}, Mesh -> None, PlotRange -> Full, PlotPoints -> 120, ContourStyle -> Directive[White, Opacity[0.3]]]] –  Maggie Sep 19 '13 at 0:02
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1 Answer

GraphicsRow[
     {ParametricPlot3D[{{t Sin@p, t Cos@p, t},
                       {{0, 0, 1 - Cos@1} + {t Sin@p, t Cos@p, Cos@t}}}, 
                       {p, 0, 2 Pi}, {t, 0, 1}, PlotRange -> {{-1, 1}, {-1, 1}, {0, 2}}],
      ParametricPlot3D[{{  Sin@p Sqrt[1 - TriangleWave[t]^2],
                           Cos@p Sqrt[1 - TriangleWave[t]^2],
                         Pi t}, 
                         {Cos[p/2], Sin[p/2], Pi t}},
                         {p, 0, 2 Pi}, {t, 0, 2}], 
      ParametricPlot3D[{Sin@p TriangleWave@t, Cos@p TriangleWave@t, 3 t},
                       {p, 0, 2 Pi}, {t, 0, 1}]}]

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