In[]:=
​​Clear[r0]​​RadiusOfCircularPlaneIntersectionWithSphere[r0_,z_]=Sqrt[r0^2-z^2]​​OblateSpheroidProfile[r0_,r_]=Solve[0==r-RadiusOfCircularPlaneIntersectionWithSphere[r0,z],z]​​r0=1​​Plot[z/.OblateSpheroidProfile[r0,r],{r,0,r0}]​​RevolutionPlot3D[z/.OblateSpheroidProfile[r0,r],{r,0,r0}]
Out[]=
2
r0
-
2
z
Solve
:There may be values of the parameters for which some or all solutions are not valid.
Out[]=
z-
-
2
r
+
2
r0
,z
-
2
r
+
2
r0

Out[]=
1
Out[]=
0.2
0.4
0.6
0.8
1.0
-1.0
-0.5
0.5
1.0
Dot
:Nonrectangular tensor encountered.
Dot
:Nonrectangular tensor encountered.
Dot
:Nonrectangular tensor encountered.
General
:Further output of Dot::rect will be suppressed during this calculation.
Out[]=