More generalized version:
newRegionPlot3D[
expr_, {u_, umin_, umax_}, {v_, vmin_, vmax_}, {w_, wmin_, wmax_},
tr_, opts___] :=
Module[{x, y, z, newExpr, xyz},
newExpr =
TransformedField[tr -> "Cartesian", expr, {u, v, w} -> {x, y, z}];
xyz = CoordinateTransform[tr -> "Cartesian", {u, v, w}];
{xmax, ymax, zmax} =
NMaxValue[{#,
umin < u < umax && vmin < v < vmax && wmin < w < wmax}, {u, v,
w}] & /@ xyz;
{xmin, ymin, zmin} =
NMinValue[{#,
umin < u < umax && vmin < v < vmax && wmin < w < wmax}, {u, v,
w}] & /@ xyz;
RegionPlot3D[
newExpr, {x, xmin, xmax}, {y, ymin, ymax}, {z, zmin, zmax}, opts]
]
Some examples:
newRegionPlot3D[
r < 1, {r, 0, 1}, {phi, 0, 2 Pi}, {th, 0, Pi}, "Spherical"]
newRegionPlot3D[
ro < 1, {ro, 0, 1}, {phi, 0, 2 Pi}, {z, 0, 1}, "Cylindrical"]