The setting is a convex cone C in R^d with the property that if u cut it with S^d the Volume of the cut is equal or greater then the Volume(S^d)/d+1 (that means the Volume of the Cone (i.e.volume of its cut with S^d) is greater or equal then the Volume of the Cone from the standard partition from R^d into d+1 Cones).

The cut of the boundary of C and S^d determines a d-1 Hyperplane. It is statet now, that the distance from this Hyperplane to the origin is less/eq 1/2.

In dimension d=2 this fact is easy to confirm by simple triangle properties. I would be very greatful though for a aproach in abitrary dimension.