Considering yours in the notebook which is `
Manipulate[
Show[RevolutionPlot3D[-x, {x, -10, 10}, RevolutionAxis -> "Z",
Boxed -> False, Axes -> False, Mesh -> None],
Graphics3D[{{Opacity[1],
White, {Rotate[
Translate[
Polygon[{{10, 10, 5}, {-10, 10, 5}, {-10, -10, 5}, {10, -10,
5}}], {0, 0, d}], a Degree, {0, 1, 0}]}}}, Boxed -> False],
ImageSize -> 270], {{d, 0, "Translation"}, -15, 5,
Appearance -> "Labeled"}, {{a, 0, "Rotation"}, 0, 145,
Appearance -> "Labeled"}]
I tried using DiscretizeGraphics, DiscretizeRegion and RegionIntersection as follows
Manipulate[
Show[RevolutionPlot3D[-x, {x, -10, 10}, RevolutionAxis -> "Z",
Boxed -> False, Axes -> False, Mesh -> None],
Graphics3D[{{Opacity[1],
White, {Rotate[
Translate[
Polygon[{{10, 10, 5}, {-10, 10, 5}, {-10, -10, 5}, {10, -10,
5}}], {0, 0, d}], a Degree, {0, 1, 0}]}}}, Boxed -> False],
DiscretizeRegion@
RegionIntersection[
DiscretizeGraphics[
RevolutionPlot3D[-x, {x, -10, 10}, RevolutionAxis -> "Z",
Boxed -> False, Axes -> False, Mesh -> None]],
DiscretizeGraphics[
Graphics3D[{{Opacity[1],
White, {Rotate[
Translate[
Polygon[{{10, 10, 5}, {-10, 10, 5}, {-10, -10,
5}, {10, -10, 5}}], {0, 0, d}], a Degree, {0, 1, 0}]}}},
Boxed -> False]]],
ImageSize -> 270], {{d, 0, "Translation"}, -15, 5,
Appearance -> "Labeled"}, {{a, 0, "Rotation"}, 0, 145,
Appearance -> "Labeled"}]
but it fails.