r^2+(h/2)^2=R^2

The lateral area of the cylinder is 2 RH.

r^2+(h/2)^2≥2*r*h/2=rh

When r=h/2, the minimum value is taken.

Rh = r 2+(h/2) 2 = the maximum value of r 2.

Maximum side area of cylinder = 2 ∏ r 2.

At this time, r=h/2, r=√2R/2.