  The aim of this paper is twofold. First, we cut off a part of a convex
surface by a plane near a ridge point and characterize the limiting behavior of
the surface measure in $S^2$ induced by this part of surface when the plane
approaches the point. Second, this characterization is applied to Newton's
least resistance problem for convex bodies: minimize the functional
$\int\int_\Omega (1 + |\nabla u(x,y)|^2)^{-1} dx dy$ in the class of convex
functions $u: \Omega \to [0,M]$, where $\Omega \subset R^2$ is a convex body
and $M > 0$. It has been known that if $u_*$ solves the problem then $|\nabla
u_*(x,y)| \ge 1$ at all regular points $(x,y)$ such that $u_*(x,y) > 0$. We
prove that if the lower level set $L_0 = \{ (x,y): u_*(x,y) = 0 \}$ has
nonempty interior, then for almost all points of its boundary $(\bar x, \bar y)
\in \partial L_0$ one has $\lim_{\stackrel{(x,y)\to(\bar x,\bar
y)}{u_*(x,y)>0}}|\nabla u_*(x,y)| = 1$.
