  Despite decades of studying the Sun, the coronal heating problem remains
unsolved. One fundamental issue is that we do not know the spatial scale of the
coronal heating mechanism. At a spatial resolution of 1000 km or more it is
likely that most observations represent superpositions of multiple unresolved
structures. In this letter, we use a combination of spectroscopic data from the
Hinode EUV Imaging Spectrometer (EIS) and high resolution images from the
Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory to
determine the spatial scales of coronal loops. We use density measurements to
construct multi-thread models of the observed loops and confirm these models
using the higher spatial resolution imaging data. The results allow us to set
constraints on the number of threads needed to reproduce a particular loop
structure. We demonstrate that in several cases million degree loops are
revealed to be single monolithic structures that are fully spatially resolved
by current instruments. The majority of loops, however, must be composed of a
number of finer, unresolved threads; but the models suggest that even for these
loops the number of threads could be small, implying that they are also close
to being resolved. These results challenge heating models of loops based on the
reconnection of braided magnetic fields in the corona.
