  The frequency of heating events in the corona is an important constraint on
the coronal heating mechanisms. Observations indicate that the intensities and
velocities measured in active region cores are effectively steady, suggesting
that heating events occur rapidly enough to keep high temperature active region
loops close to equilibrium. In this paper, we couple observations of Active
Region 10955 made with XRT and EIS on \textit{Hinode} to test a simple steady
heating model. First we calculate the differential emission measure of the apex
region of the loops in the active region core. We find the DEM to be broad and
peaked around 3\,MK. We then determine the densities in the corresponding
footpoint regions. Using potential field extrapolations to approximate the loop
lengths and the density-sensitive line ratios to infer the magnitude of the
heating, we build a steady heating model for the active region core and find
that we can match the general properties of the observed DEM for the
temperature range of 6.3 $<$ Log T $<$ 6.7. This model, for the first time,
accounts for the base pressure, loop length, and distribution of apex
temperatures of the core loops. We find that the density-sensitive spectral
line intensities and the bulk of the hot emission in the active region core are
consistent with steady heating. We also find, however, that the steady heating
model cannot address the emission observed at lower temperatures. This emission
may be due to foreground or background structures, or may indicate that the
heating in the core is more complicated. Different heating scenarios must be
tested to determine if they have the same level of agreement.
