graphics3d - Plotting Semi-hollow spheres

I wish to create a nice data representation of three nested spherical sections, with a cut away so they can be viewed. As a MWE, something like;

a = SphericalPlot3D[{1}, {θ, 0, Pi}, {ϕ, 0, 4 Pi/2}, 
   PlotStyle -> Directive[Blue, Opacity[0.7], Specularity[White, 20]],
    Mesh -> None, PlotPoints -> 40];


b = SphericalPlot3D[{2}, {θ, 0, Pi}, {ϕ, 0, 3 Pi/2}, 
   PlotStyle -> Directive[Red, Opacity[0.7], Specularity[White, 20]], 
  Mesh -> {{0}, {0}, {0}}, PlotPoints -> 40];

c = SphericalPlot3D[{3}, {θ, 0, Pi}, {ϕ, 0, 3 Pi/2}, 
   PlotStyle -> 
   Directive[Green, Opacity[0.7], Specularity[White, 20]], 
  Mesh -> {{0}, {0}, {0}}, PlotPoints -> 40];

abc = Show[a, b, c, PlotRange -> Automatic]

This gives me the following image, after some rotation for clarity;

This is kind of the idea, but the problem is that this displays as spherical surfaces at r = 1, r = 2 and r = 3. In reality, there is a thick spherical shell (let's say a red one) for $1 \leq r \leq 2$ and a thick spherical shell (a green one) at $2 \leq r \leq 3$. The spherical core at $r \leq 1$ is solid blue. Is there a nice way to make this image? I was hoping I could somehow modify the $r$ term in the SphericalPlot3D function to do this.

I could also like to add a vertical line running through the sphere centre (z = 0) to make the image clearer. Any ideas?

Thanks

Answer

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]

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

Edit

With the new V10 function ClipPlanes you can easily slice your graphics:

Grid[

 {{
   Show[p1, p2, p3, p4, p5, ClipPlanes -> {{-1, 1, 0, 1}}, ImageSize -> 400],
   Show[p1, p2, p3, p4, p5, ClipPlanes -> {{0, 0, -1, 0}}, ImageSize -> 400]
   }}]