  We investigate a point-like massive source in non-linear f(R) theories in the
case of arbitrary number of spatial dimensions D\geq 3. If D>3 then extra
dimensions undergo toroidal compactification. We consider a weak-field
approximation with Minkowski and de Sitter background solutions. In both these
cases point-like massive sources demonstrate good agreement with experimental
data only in the case of ordinary three-dimensional (D=3) space. We generalize
this result to the case of perfect fluid with dust-like equations of state in
the external and internal spaces. This perfect fluid is uniformly smeared over
all extra dimensions and enclosed in a three-dimensional sphere. In ordinary
three dimensional (D=3) space, our formulas are useful for experimental
constraints on parameters of f(R) models.
