7
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GraphicsRow[
 {Plot3D[x^2 + y^2, {x, -6, 6}, {y, -6, 6}, PlotRange -> Automatic], 
  Plot3D[x^2 + y^2, {x, -6, 6}, {y, -6, 6}, 
   PlotRange -> {{-6, 6}, {-6, 6}, {0, 30}}],
  Plot3D[x^2 + y^2, {x, -6, 6}, {y, -6, 6}, 
   PlotRange -> {Full, Full, {0, 30}}]}, ImageSize -> 700]

yields

enter image description here

How do I get the full "bowl" look without the extra flat part filling out the plane at $z=30$? I must be missing something simple...

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14
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Use the ClippingStyle option to control the appearance of the cut off part.

Plot3D[x^2 + y^2, {x, -6, 6}, {y, -6, 6}, 
 PlotRange -> {{-6, 6}, {-6, 6}, {0, 30}}, ClippingStyle -> None]

Mathematica graphics

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