# How to combine 3D graphics

I'm trying to put this solid S1 = RegionPlot3D[z - 50 <= -2 x^2 - 2 y^2, {x, -5, 5}, {y, -5, 5}, {z, 0, 50}]


on top of this one S2 =
RegionPlot3D[x^2 + y^2 <= 50 , {x, -10, 10}, {y, -10, 10}, {z, -50, 0},
PlotStyle -> RGBColor[0.15, 0.17, 0], Mesh -> None]


and it's just kind of smashing it into this

Show[
RegionPlot3D[
z <= -2 x^2 - 2 y^2 && z <= 8 x + y - 20,
{x, -10, 10}, {y, -10, 10}, {z, -100, 0}],
RegionPlot3D[x^2 + y^2 <= 50 , {x, -10, 10}, {y, -10, 10}, {z, -500, -100},
PlotStyle -> RGBColor[0.15, 0.17, 0], Mesh -> None]] How to combine these 3D plots correctly?

Try this

With[{color = RGBColor[0.95, 0.93, 0]},
Show[
RegionPlot3D[
z <= -2 x^2 - 2 y^2 && z <= 8 x + y - 20,
{x, -10, 10}, {y, -10, 10}, {z, -100, 0},
PlotStyle -> color, Mesh -> None],
RegionPlot3D[
x^2 + y^2 <= 50,
{x, -10, 10}, {y, -10, 10}, {z, -500, -100},
PlotStyle -> color, Mesh -> None],
PlotRange -> All]] Your problem was mainly not giving the option PlotRange -> All to Show. Without that, you were only getting the range for first RegionPlot3D.

I changed the coloring only to get a better looking plot for this post. It not a part of your problem. You can choose any color you like.

Another way can be defining a single function

f[x_, y_, z_] := If[z > 0, z - 50 <= -2 x^2 - 2 y^2, x^2 + y^2 <= 50]
RegionPlot3D[f[x, y, z], {x, -10, 10}, {y, -10, 10}, {z, -50, 50}] 