I've thought of a method but I dun know whether it works or
not.
You consider the top part of the sphere that is not filled by
water. Observe that in 2-dimensional drawing, it's cutting off the
top part of a circle.
Now consider an x-y axis graph, line up this top part such that the
straight line coincides with the y axis. I think if you were to
reflect this graph along the y axis, you'll get an ellipse and thus
you can determine the actual equation of this curve.
Now if I recall, you can integrate this curve from x = 0 to x = 3.5
and consider a 360 degrees rotation along the x-axis to get the
volume of this cut-off part. But exact method escapes me at the
moment. 
Thus, you can determine the full sphere volume and the volume you
want is just the full volume - volume of top part, then just divide
by 10 to get the answer.
Hmmm....is that it? 
