(Software) Drawing spherical coordinates - triple integrals

Question

How can I create figures such as the following:

Is there a LaTeX solution?

I tried using GeoGebra but it didn't work.

Any help is appreciated.

Cheers,

Answer 1

Mathematica:

Graphics3D[{Cone[{{0, 0, 1}, {0, 0, 0}}, 1/2], 
  Cylinder[{{0, 0, 0}, {0, 0, .001}}, 1/2]},
  PlotRange -> {{-1/2, 1/2}, {-1/2, 1/2}, {0, .99}},
  Axes -> Automatic,
  AxesOrigin -> {0, 0, 0},
  Boxed ->False]

and

surf = ParametricPlot3D[{r Cos[\[Theta]], r Sin[\[Theta]], r},
   {\[Theta], 0, \[Pi]/2}, {r, 0, 1},
   PlotRange -> {{-1, 1}, {-1, 1}, {0, 1}},
   Mesh -> None,
   AxesOrigin -> {0, 0, 0}];
ring = ParametricPlot3D[{Cos[\[Theta]], Sin[\[Theta]], 1},
   {\[Theta], 0, 2 \[Pi]},
   PlotStyle -> Directive[Thickness[0.01], Red]];
Show[{surf, ring}]