Mean Chord Length of Convex 3D Shape

dsr39

One of my homework problems asks me to use the fact that the mean chord length of a convex 3d shape is equal to:

4V/S

where V = Volume and S = surface area.

I was just wondering if anyone could provide me with or point me to a proof of this fact. I think I could probably manage a proof for the specific case of a sphere (though it doesn't seem like it would be a pretty calculation) but I am looking for the general proof for any convex shape.