  We obtain sharp volume bound for a conic 2-sphere in terms of its Gaussian
curvature bound. We also give the geometric models realizing the extremal
volume. In particular, when the curvature is bounded in absolute value by $1$,
we compute the minimal volume of a conic sphere in the sense of Gromov. In
order to apply the level set analysis and iso-perimetric inequality as in our
previous works, we develop some new analytical tools to treat regions with
vanishing curvature.
