The spatial geometry difficulty of mathematics problems in senior one is moderate.
Let the radius of the bottom surface of the cylinder be r.
x/6=(2-r)/2
r=2-x/3
Axial sectional area s = 2r * x = 2 (2-x/3) * x =-2/3x 2+4x.
S'=-4/3x+4 ream S'=0 x=3
So when x=3, Smax=6.