  The radii and orbital periods of 4000+ confirmed/candidate exoplanets have
been precisely measured by the Kepler mission. The radii show a bimodal
distribution, with two peaks corresponding to smaller planets (likely rocky)
and larger intermediate-size planets, respectively. While only the masses of
the planets orbiting the brightest stars can be determined by ground-based
spectroscopic observations, these observations allow calculation of their
average densities placing constraints on the bulk compositions and internal
structures. Yet an important question about the composition of planets ranging
from 2 to 4 Earth radii still remains. They may either have a rocky core
enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant
amount of multi-component, H2O-dominated ices/fluids (water worlds). Planets in
the mass range of 10-15 Earth masses, if half-ice and half-rock by mass, have
radii of 2.5 Earth radii, which exactly match the second peak of the exoplanet
radius bimodal distribution. Any planet in the 2-4 Earth radii range requires a
gas envelope of at most a few mass percentage points, regardless of the core
composition. To resolve the ambiguity of internal compositions, we use a growth
model and conduct Monte Carlo simulations to demonstrate that many
intermediate-size planets are water worlds.
