Wolfram Cloud Document

Apple::usage="The curve 

2y+10±

-8+64y-32

2

y

6

,

2y+10±

-8+64y-32

2

y

6

,y, it rotatesaround the line x = y = z. Reference: Personal.";

Development:

Reduce[-8+64y-32

2

y

>=0,y]

1

2

2-

3

≤y≤

1

2

2+

3



In[]:=

ManipulateShowRevolutionPlot3D

2y+10+

-8+64y-32

2

y

6

,

2y+10+

-8+64y-32

2

y

6

,y,

2y+10-

-8+64y-32

2

y

6

,

2y+10-

-8+64y-32

2

y

6

,y,y,

1

2

2-

3

,

1

2

2+

3

,{θ,0,θ1},RevolutionAxis{1,1,1},PlotStyle->Opacity[0.8],MeshFalse,PerformanceGoal"Quality",ColorFunction"LightTemperatureMap",BoxRatiosAutomatic,PlotRange3.1,BoxedFalse,ViewPoint{-1.3,-2.4,60},ImageSize700,Style["Apple:",Bold,Large],{{θ1,0.1,"Value (θ)"},0.01,2π,0.1},ControlPlacementTop

Out[]=

Apple:

Value (θ)