AreaSpheresPlane::usage="Calculate the area in red (visualize the figure in 3D).​
​References: Internet: Ronny on line (figure)​; Personal.";
Development for surface area:
In[]:=
ℜ=ImplicitRegion[
2
x
+
2
y
+
2
z
<=16
2
π
&&
2
(x-2π)
+
2
y
+
2
z
>=4
2
π
&&x>=2π&&z>=0,{x,y,z}];​​SurfaceArea[ℜ]
-
2
3
6
3
2
π
-29
3
π
;
Animation:
In[]:=
Manipulate[Show[RegionPlot3D[
2
x
+
2
y
+
2
z
<=16
2
π
&&
2
(x-2π)
+
2
y
+
2
z
>=4
2
π
&&x>=2π&&z>=0,{x,2π,4π},y,-2
3
π,2
3
π,{z,0,t1},MeshNone,PerformanceGoal->"Quality",PlotPoints60,PlotStyleDirective[Red,Opacity[0.3],Specularity[White,40]]],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRange{2π,4π},-2
3
π,2
3
π,0,2
3
π,ViewPoint{-1,-2.4,1.},ImageSize700],Style["Area section between spheres and planes:",Bold,Large],{t1,0.00002,"Value (t1)"},0.00001,2
3
π,0.00001,ControlPlacementTop]
Out[]=
​
Area section between spheres and planes:
Value (t1)