Code:

pic1 = Graphics3D[
{Polygon[{{2, 2, 0}, {-2, 2, 0},
{-2, -2, 0}, {2, -2, 0},
{2, 2, 0}}], Polygon[{{1, 0, 0},
{1, 1, 0}, {1, 1, 1}, {1, 0, 1},
{1, 0, 1}}], Line[{{-2, 0, 0},
{2, 0, 0}}], Line[{{0, 2, 0},
{0, -2, 0}}], Line[{{1, 1, 0},
{Sqrt[3], 1, 0}}],
Line[{{1, 0, 0}, {1, 1, 0}}],
Line[{{1, 1, 1}, {Sqrt[2], 1, 1}}],
Line[{{1, 0, 1}, {Sqrt[3], 0,
1}}]}];
bottom = ContourPlot3D[x^2 + y^2 + z^2 ==
4, {x, -2, 2}, {y, -2, 2}, {z, 0, 1},
PlotRange -> {{-2, 2}, {-2, 2},
{-2, 2}}, BoxRatios -> {1, 1, 1},
ContourStyle -> {Opacity[0.2], Red},
Mesh -> None]
shellsurface = ContourPlot3D[
x^2 + y^2 + z^2 == 4, {x, -2, 2},
{y, -2, 2}, {z, 0, 1}, PlotRange ->
{{-2, 2}, {-2, 2}, {-2, 2}},
BoxRatios -> {1, 1, 1},
ContourStyle -> {Opacity[0.2], Red},
Mesh -> None, RegionFunction ->
Function[{x, y, z}, 1 <= x <= 2 &&
0 <= y <= 1 && 0 <= z <= 1]]
Show[{bottom, pic1, shellsurface}]