drawing core-shell structure

Show[RegionPlot3D[1 <= x^2 + y^2 + z^2 <= 3 && (y >= x Sin[Pi/2] || y < -x Sin[Pi/2]),   
                  {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Mesh -> None, PlotPoints -> 100], 
     Graphics3D[{Red, Sphere[{0, 0, 0}, 1]}]]

SetOptions[{SphericalPlot3D, ParametricPlot3D}, Mesh -> None];

fun = {r {0, -Sin[t], Cos[t]}, r {Sin[t], 0, Cos[t]}};

p1 = SphericalPlot3D[{2, 2.5}, {u, 0, Pi}, {v, 0, 1.5 Pi}, 
   PlotStyle -> 
    Directive[Green, Opacity[0.7], Specularity[White, 20]]];

p2 = ParametricPlot3D[fun, {r, 2, 2.5}, {t, 0, Pi}, 
   PlotStyle -> 
    Directive[Green, Opacity[0.7], Specularity[White, 20]]];

p3 = SphericalPlot3D[{1.5, 1.99}, {u, 0, Pi}, {v, 0, 1.5 Pi}, 
   PlotStyle -> Directive[Red, Opacity[0.7], Specularity[White, 20]]];

p4 = ParametricPlot3D[fun, {r, 1.5, 1.99}, {t, 0, Pi}, 
   PlotStyle -> Directive[Red, Opacity[0.7], Specularity[White, 20]]];

p5 = SphericalPlot3D[{1, 1.48}, {u, 0, Pi}, {v, 0, 2 Pi}, 
   PlotStyle -> Directive[Blue, Opacity[0.7], Specularity[White, 20]]];

Show[p1, p2, p3, p4, p5, PlotRange -> All, Axes -> False, 
 Boxed -> False]

Show[p1, p2, p3, p4, p5, PlotRange -> All, ViewPoint -> Front]

 Grid[{{

   Show[p3, p4, p5, ClipPlanes -> {{-1, 1, 0, 1}},
    Axes -> False, Boxed -> False, ImageSize -> 400],

   Show[p3, p4, p5, ClipPlanes -> {{0, 0, -1, 0}},
    Axes -> False, Boxed -> False, ImageSize -> 400]}}]

 p = N@Table[  { Cos[x], 0, Sin[x]}, {x, Pi/2, -Pi/2, -Pi/200}];
 Show[ 
      {
     SphericalPlot3D[ 1 , {t, 0, Pi}, {phi, 0, 3 Pi/2}, Axes -> False, Mesh -> False],
     Graphics3D@{{Red, Sphere[{0, 0, 0}, 1/2]},
                 Polygon[ p],
                 Polygon@(RotationTransform[-Pi/2, {0, 0, 1}]@p)
         }} , Boxed -> False ]