For a pinhole I can conceptualize the image formation by drawing straight lines from the subject to the film via the pinhole. But I'm not sure what the image would look like for a lens given that the film is parallel to the optical axis. Something similar surely when the aperture is stopped down, but still I think you would get a only narrow band where the subject is in focus. Or maybe it's okay if the subject is parallel to the axis as well. Could be cool.
The length of the frame would be decided by the diameter of the cylinder, and the diameter by the image circle of the lens, not the focal length I think. I think this a 6x6 enlarger lens, so ~80mm diameter circle, meaning a 250mm circumference.