  We report the discovery of a new ultra-short-period planet and summarize the
properties of all such planets for which the mass and radius have been
measured. The new planet, EPIC~228732031b, was discovered in {\it K2} Campaign
10. It has a radius of 1.81$^{+0.16}_{-0.12}~R_{\oplus}$ and orbits a G dwarf
with a period of 8.9 hours. Radial velocities obtained with Magellan/PFS and
TNG/HARPS-N show evidence for stellar activity along with orbital motion. We
determined the planetary mass using two different methods: (1) the "floating
chunk offset" method, based only on changes in velocity observed on the same
night, and (2) a Gaussian process regression based on both the radial-velocity
and photometric time series. The results are consistent and lead to a mass
measurement of $6.5 \pm 1.6~M_{\oplus}$, and a mean density of
$6.0^{+3.0}_{-2.7}$~g~cm$^{-3}$.
