  The galaxy size-stellar mass and central surface density-stellar mass
relationships are observational constraints on galaxy formation models.
However, inferring the physical size of a galaxy from observed stellar emission
is non-trivial due to various observational effects. Consequently,
forward-modeling light-based sizes from simulations is desirable. In this work,
we use the {\skirt} dust radiative transfer code to generate synthetic
observations of massive galaxies ($M_{*}\sim10^{11}\,\rm{M_{\odot}}$ at $z=2$,
hosted by haloes of mass $M_{\rm{halo}}\sim10^{12.5}\,\rm{M_{\odot}}$) from
high-resolution cosmological zoom-in simulations that form part of the Feedback
In Realistic Environments (FIRE) project. The simulations used in this paper
include explicit stellar feedback but no active galactic nucleus (AGN)
feedback. From each mock observation, we infer the effective radius ($R_e$), as
well as the stellar mass surface density within this radius and within
$1\,\rm{kpc}$ ($\Sigma_e$ and $\Sigma_1$, respectively). We first investigate
how well the intrinsic half-mass radius and stellar mass surface density can be
inferred from observables. The predicted sizes and surface densities are within
a factor of two of the intrinsic values. We then compare our predictions to the
observed size-mass relationship and the $\Sigma_1-M_\star$ and
$\Sigma_e-M_\star$ relationships. At $z\gtrsim2$, the simulated massive
galaxies are in general agreement with observational scaling relations. At
$z\lesssim2$, they evolve to become too compact but still star-forming, in the
stellar mass and redshift regime where many of them should be quenched. Our
results suggest that some additional source of feedback, such as AGN driven
outflows, is necessary in order to decrease the central densities of the
simulated massive galaxies to bring them into agreement with observations at
$z\lesssim2$.
