In case the goal is to draw points inside the sphere, the discussion 
https://mathoverflow.net/questions/33129/intuitive-proof-that-the-first-n-2-coordinates-on-a-sphere-are-uniform-in-a-bal
seems relevant.

In other words, one simply draws random points on the 10-dimensional sphere (by drawing a normal vector and normalizing it) and discards the last two coordinates.