Imagine the liquid became solidified.
Rotate the can until the face which contains XY is
Now take the horizontal cross-section half way up the can
which meets the plane face of the "liquid" in the line AB.
Observing that AB bisects the radius PQ, rotate the upper
section of the "liquid" about AB through 180 degrees. The new
position is shaded darkly and fits into the bottom right hand
quarter (with some space to spare).
The actual fraction can be shown to be approximately 0.21. The
answer is therefore less than a quarter.
This problem is taken from the UKMT Mathematical Challenges.