I'm asking if there is a way to animate a function $f(x)$ (plotted in a range $(a, b)$ with $a > 0$ and $b > 0$), making it to revolve around the $Y$ axis and showing the solid of revolution obtained in this way.
For example, say $f(x) = 1/x$ in the range $x\in(1, 5)$. I know how to plot the solid of revolution obtained from this, but it's the animation part, if possible, that I would like to understand.
Thank you!
To make things clarer: a code like this would workg well
Manipulate[
Show[
ParametricPlot3D[{u^2, 0, u}, {u, 0, 1},
PlotStyle -> Directive[Red, Thick]],
RevolutionPlot3D[Sqrt[x], {x, 0, 1}, {t, 0, T},
PlotStyle -> {Opacity[.5], Specularity[White, 10]},
ColorFunction -> "Rainbow", MeshStyle -> Opacity[.3],
MeshShading -> ms, PlotPoints -> 30]
, Axes -> True, Boxed -> False, BoxRatios -> {1, 1, 1.5},
AxesOrigin -> {0, 0, 0}, PlotRange -> {{-1, 1}, {-1, 1}, {0, 1}},
ViewPoint -> {1.1, 2.6, 1.73}, ViewVertical -> {1.4, 0.3, 0.2},
SphericalRegion -> True, ViewAngle -> .4, ImageSize -> 600,
AxesStyle -> Directive[Black, Thick]]
, {{ms, None,
"shades"}, {None -> "NO", {{Red, Yellow}, {Pink, Orange}} -> "YES"}}
, {{T, 2 Pi}, .001, 2 Pi, Appearance -> "Labeled"},
FrameMargins -> 0]
Just needs to be adapted to a revolution around $Y$ axis, and to other possible functions.
( Taken from RevolutionPlot3D: but NOT revolving about the z axis )
