RegionPlot3D[x^2+y^2<1&&0<z<x+3,{x,-1.2,1.2},{y,-1.2,1.2},{z,-.2,4.2},Mesh->None,PlotStyle->Directive[Specularity[White, 10],Opacity[0.85],Purple],PlotPoints->50,AxesLabel->Automatic]

p2=Plot3D[x^2+y^2,{x,-√2-.1,√2+.1},{y,-√2-.1,√2+.1},Mesh->None,PlotStyle->Directive[Specularity[White, 10],Opacity[0.65],Purple],BoxRatios->Automatic];
p3=Plot3D[√(6-x^2-y^2),{x,-√6-.1,√6+.1},{y,-√6-.1,√6+.1},Mesh->None,PlotStyle->Directive[Specularity[White, 10],Opacity[0.65],Purple],BoxRatios->Automatic];

Show[p3,p2]

p1=RegionPlot3D[x^2+y^2<z<√(6-x^2-y^2),{x,-√2-.3,√2+.3},{y,-√2-.3,√2+.3},{z,-.3,√6+.3},Mesh->None,PlotStyle->Directive[Specularity[White, 10],Opacity[0.85],Purple],PlotPoints->50,AxesLabel->Automatic,BoxRatios->Automatic]

p4=RegionPlot3D[x^2+y^2+z^2<1,{x,-1,1},{y,-1,1},{z,0,1},Mesh->None,PlotStyle->Directive[Specularity[White, 10],Opacity[0.65],Purple],PlotPoints->50,AxesLabel->Automatic,BoxRatios->Automatic];

p5=RegionPlot3D[x^2+y^2<.5z^2&&z>0,{x,-.7,.7},{y,-.7,.7},{z,0,1},Mesh->None,PlotStyle->Directive[Specularity[White, 10],Opacity[0.65],Purple],PlotPoints->50,AxesLabel->Automatic,BoxRatios->Automatic];

Show[p4,p5]

RegionPlot3D[x^2+y^2+z^2<1&&x^2+y^2<.5z^2&&z>0,{x,-.6,.6},{y,-.6,.6},{z,0,1},Mesh->None,PlotStyle->Directive[Specularity[White, 10],Opacity[0.85],Purple],PlotPoints->50,AxesLabel->Automatic,BoxRatios->Automatic]

RegionPlot3D[x^2+y^2+z^2<9&&x>0&&y>0&&z>0,{x,0,3},{y,0,3},{z,0,3},Mesh->None,PlotStyle->Directive[Specularity[White, 10],Opacity[0.85],Purple],PlotPoints->50,AxesLabel->Automatic,BoxRatios->Automatic]