Many interesting systems of nanometer dimensions form spherically symmetric domains, either by design or through spontaneous self-assembly. The technique of direct nonradiative resonance energy transfer (DET) can be used to characterize the morphology of such structures on a nanometer scale. One needs to label the domain of interest with appropriate donor and acceptor dye moieties. One measures the fluorescence decay of the donors (I-D(t)) in the presence of accepters. The underlying geometry and physics of the system dictate how the dyes distribute themselves along the radial axis R of the system, according to concentration profiles (C-D(R), and C-A(R)) which need not be uniform. Because DET is sensitive to the distribution of dye interdistances, I-D(t) contains information about the underlying morphology. In this work we obtain an analytic expression relating I-D(t) to the donor/acceptor concentration profiles. This extends our previous contribution for systems with a plane of symmetry. The expression developed is general and capable of handling geometries in both extended and/or restricted spaces. It does not require a specific spatial locus for the donors nor does it require prior calculation of the pair-distribution function of the donor-acceptor distances. The development also provides one with an analytic expression for the evaluation of the interdistance distribution functions.