The classical isoperimetric problem for volumes is solved in R x S-n(1). Minimizers are shown to be invariant under the group O(n) acting standardly on S-n, via a symmetrization argument, and are then classified. Solutions are found among two ( one-parameter) families: balls and sections of the form [ a, b] x S-n. It is shown that the minimizers may be of both types. For n = 2, it is shown that the transition between the two families occurs exactly once. Some results for general n are also presented.264333354