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We develop a simple analytical theory that relates dense sphere packings in a cylinder to corresponding disk packings on its surface. It applies for ratios R=D/d (where d and D are the diameters of the hard spheres and the bounding cylinder, respectively) up to R=1+1/sin(pi/5). Within this range the densest packings are such that all spheres are in contact with the cylindrical boundary. The detailed results elucidate extensive numerical simulations by ourselves and others by identifying thedoi:10.1103/physrevlett.106.115704 pmid:21469881 fatcat:57lhaz3yunaadgfewc5s4m6eiy