AreaDeSuperficieDeRevolucion14::usage="Find the surface area of the surface that is generated when the curve x = 1 + 2
2
y
​, 1 ≤ y ≤ 2 rotates around the X axis. References: Personal.";
In[]:=
ManipulateClearAll;ShowRevolutionPlot3Dx,
1
2
(x-1)
,0,{x,3,9},{θ,0,θ1},RevolutionAxis{1,0,0},PlotStyle->Opacity[0.6],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow",ParametricPlot3D[t{1,0,0},{t,-1,10},ColorFunction->"BlueGreenYellow"],Graphics3D[{Black,Ball[{3,0,0},0.05]}],Graphics3D[{Black,Ball[{3,Cos[θ1],Sin[θ1]},0.05]}],​​Graphics3D[{Black,Dashed,Thick,Line[{{3,0,0},{3,Cos[θ1],Sin[θ1]}}]}],Graphics3D[{Black,Ball[{9,0,0},0.05]}],Graphics3D[{Black,Ball[{9,2Cos[θ1],2Sin[θ1]},0.05]}],​​Graphics3D[{Black,Dashed,Thick,Line[{{9,0,0},{9,2Cos[θ1],2Sin[θ1]}}]}],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ViewPoint{1.3,-2.4,2.},ImageSizeFull,Style["Revolution surface:",Bold,Large],{{θ1,1,"Value (θ)"},0.1,2π,0.1},ControlPlacementTop
Out[]=
​
Revolution surface:
Value (θ)
Surface revolution area:
In[]:=
f[x_]:=
1
2
(x-1)
;
In[]:=
A=N
9
∫
3
2πf[x]
1+
2
(f'[x])
x
Out[]=
59.4224
In[]:=
ContourPlot3D[x==1+2(
2
y
+
2
z
),{x,3,9},{y,-2,2},{z,-2,2},BoxRatios->Automatic]
Out[]=
The equation of the surface of revolution is:
x=1+2
2
y
+
2
z

.
​