Revolving a region about the x-axis

Questions
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1

Hi, everyone, I have the next problem, let R be region bounded by y = 12-x^3 and y=12-4x, find the volume generated by revolving R about x-axis, what interests me is to rotate about the x axis, the next intersection

Plot[{12 - x^3, 12 - 4 x}, {x, -2, 2}, 
 Filling -> {1 -> {{2}, Yellow}}]

but not how to do it, I hope someone has a suggestion,I’m interested in the 3D graphic

2

Hi,

are you looking for something like this?

Show[RevolutionPlot3D[12 - x^3, {x, -2, 2}, {theta, 0, 2 Pi}, 
  RevolutionAxis -> {1, 0, 0}, AspectRatio -> 1], 
 RevolutionPlot3D[12 - 4 x, {x, -2, 2}, {theta, 0, 2 Pi}, 
  RevolutionAxis -> {1, 0, 0}, AspectRatio -> 1]]

Revolution3d.jpg
Revolution3d.jpg554×488 40.7 KB

M.

3

Exactly what I need, please help me resolve my doubt.