How can I draw a barrel like this?

Question

I see this picture about Barrel

I tried

RevolutionPlot3D[-0.011*x^2 - 0.071*x + 40, {x, -35, 35}, 
 RevolutionAxis -> {1, 0, 0}, Boxed -> False, Axes -> False]

I got

Answer 1

texture = Texture[ImageMultiply[ExampleData[{"Texture", "Wood"}], Orange]];

Graphics3D[{CapForm["Butt"], FaceForm[texture], 
  Tube[BezierCurve @ {{0, 0, 0}, {0, 0, 1}, {0, 0, 2}}, {.8, 1, .8}], 
  MaterialShading["Aluminum"], 
  Tube[{{0, 0, 1.8}, {0, 0, 2}}, {.85, .82}], 
  Tube[{{0, 0, .2}, {0, 0, 0}}, {.85, .82}], 
  Tube[BezierCurve @ {{0, 0, 1.1}, {0, 0, 1}, {0, 0, 0.9}}, .92]}, 
 Boxed -> False, Lighting -> "ThreePoint", ImageSize -> Large]

Answer 2

An attempt:

e1 = Ellipsoid[{0, 0, 0}, {5, 3, 3}];
cb1 = Cuboid[{-3, -3, -3}, {3, 3, 3}];
Graphics3D[{e1, cb1}]

sr = ShellRegion[DiscretizeRegion@RegionIntersection[e1, cb1], 0.2];
Graphics3D[{Opacity[0.3], sr}, Boxed -> False]

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