sphtor[sphrho_,sphtheta_,sphphi_] = {sphrho*Sin[sphphi]*Cos[sphtheta],sphrho*Sin[sphphi]*Sin[sphtheta],sphrho*Cos[sphphi]};r1=ParametricPlot3D[sphtor[5,theta,phi],{theta,0,2*Pi},{phi,0,Pi/2},Mesh->50,MeshStyle->Opacity[0]];
r2=ParametricPlot3D[sphtor[3,theta,phi],{theta,0,2*Pi},{phi,0,Pi/2},Mesh->50,MeshStyle->Opacity[0]];
hring=ParametricPlot3D[sphtor[rho,theta,Pi/2],{theta,0,2*Pi},{rho,3,5},Mesh->50,MeshStyle->Opacity[0]];
tp=Show[{r1,r2,hring},Boxed->False,AxesLabel->{"X","Y","Z"},ViewPoint->{1,-0.5,-0.8}]

Export["dome_half_spherical_shell.png",tp, ImageSize->500];