Example 1: Cylindrical Shells

g[x_]:=(Sqrt[x])

Plot[{g[x]},{x,0,1},PlotRange->2]

Rotate about the y-axis ... get cloud city.

Show[{
RevolutionPlot3D[g[x],{x,0,1}]},PlotRange->1]

Δ=0.1;
Manipulate[Show[{
RevolutionPlot3D[g[x],{x,r,r+Δ}],
ParametricPlot3D[{r Cos[θ],r Sin[θ],t},{θ,0,2π},{t,0,g[r]}],
ParametricPlot3D[{(r +Δ)Cos[θ],(r +Δ) Sin[θ],t},{θ,0,2π},{t,0,g[(r +Δ)]}],
ParametricPlot3D[{{x,0,g[x]}},{x,0,1}]},PlotRange->{0,1},Ticks->False],{r,Δ,1-2Δ,Δ}]

Example 2: Cylindrical shells between curves

f[x_]:=(x^3)
g[x_]:=(Sqrt[x])

Plot[{f[x],g[x]},{x,0,1},PlotRange->2]

Rotate about the y-axis ... get a flower-bowl-thingy

Show[{RevolutionPlot3D[f[x],{x,0,1}],
RevolutionPlot3D[g[x],{x,0,1}]},PlotRange->1]

Add a mushroom stem for kicks

stem[x_]:=10x
Show[{RevolutionPlot3D[f[x],{x,0,1}],
RevolutionPlot3D[g[x],{x,0,1}],
RevolutionPlot3D[stem[x],{x,0,1}]},PlotRange->2]

Δ=0.1;
Manipulate[Show[{RevolutionPlot3D[f[x],{x,r,r+Δ}],
RevolutionPlot3D[g[x],{x,r,r+Δ}],
ParametricPlot3D[{r Cos[θ],r Sin[θ],t},{θ,0,2π},{t,f[r],g[r]}],
ParametricPlot3D[{(r +Δ)Cos[θ],(r +Δ) Sin[θ],t},{θ,0,2π},{t,f[(r +Δ)],g[(r +Δ)]}],
ParametricPlot3D[{{x,0,f[x]},{x,0,g[x]}},{x,0,1}]},PlotRange->1],{r,Δ,1-2Δ,Δ}]

Example 3: Rotate the region about the line x=-1

f[x_]:=(x^3)
g[x_]:=(Sqrt[x])

The region

Plot[{f[x],g[x]},{x,0,1},PlotRange->2]

Rotate about the line x=-1 ... get a nice ring thingy

Show[{RevolutionPlot3D[{x,f[x-1]},{x,1,2}],
RevolutionPlot3D[{x,g[x-1]},{x,1,2}]},PlotRange->{0,1},Ticks->False]

Here are the cylindrical shells.

Δ=0.1;
Manipulate[Show[{(*lower curve*)RevolutionPlot3D[{x,f[x-1]},{x,r+1,r+Δ+1}],
(*upper curve*)RevolutionPlot3D[{x,g[x-1]},{x,r+1,r+Δ+1}],
(*inside wall*)ParametricPlot3D[{(r+1) Cos[θ],(r+1) Sin[θ],t},{θ,0,(3/2)π},{t,f[r],g[r]}],
(*outside wall*)ParametricPlot3D[{(r +Δ+1)Cos[θ],(r +Δ+1) Sin[θ],t},{θ,0,(5/4)π},{t,f[(r +Δ)],g[(r +Δ)]}],

(*f and g*)ParametricPlot3D[{{x,0,f[x-1]},{x,0,g[x-1]},{0,0,x-1}},{x,1,2}]},PlotRange->{0,1},Ticks->False],{r,Δ,1-2Δ,Δ}]