V_S
= the volume of water which is displaced by the largest small sphere
= the height of the green line segment

V_M
= the volume of water which is displaced by the optimal medium sphere
= the height of the blue line segment

V_L
= the volume of water which is displaced by the smallest large sphere
= the height of the right end of the yellow curve

claim:
If h = 5 and θ = π/7, then V_S < V_L < V_M.

proof:
Inspect the image.