Ok, y-axis. You have to build them up although there may be an easier way to do that. Here's what I came up with. The second is a cross-section of the volume of revolution.

Code:

cyl = ParametricPlot3D[{4*Cos[t], 4*Sin[t],
z}, {t, 0, 2*Pi}, {z, 8, 16}]
p1 = RevolutionPlot3D[{x^2}, {x, 2, 4},
BoxRatios -> {1, 1, 1}, PlotStyle -> Red]
p2 = RevolutionPlot3D[{2*x}, {x, 2, 4},
BoxRatios -> {1, 1/4, 1},
PlotStyle -> Blue]
fig1 = Show[{p1, p2, cyl}]
fig2 = Show[{p1, p2, cyl}, PlotRange ->
{{-4, 4}, {0, 4}, {0, 16}}]
GraphicsArray[{{fig1, fig2}}]