https://nrich.maths.org/2664 To make cylinders of varying sizes, the three pieces can be cut from a single rectangle of flat sheet in several ways.
Can you work out some possible dimensions of a rectangle and two circles which can be cut from a single sheet of 8.5 x 11-inch paper and put together to make a cylinder? The link says A4 paper but I'm using 8.5 x 11 inch
Which dimensions allow you to make a cylinder with the greatest volume?
The page you link to shows two configurations for the rectangle and the circles. Let $r$ be the radius of the circles. You should be able to compute the size of the rectangle based on $r$, then the volume of the cylinder. Take the derivative, set to zero ... Try it for each configuration and convince yourself there is no other configuration that is better.