Distributions sensitive to the underlying event are studied in events containing one or more chargedparticle jets produced in pp collisions at root s = 7 TeV with the ATLAS detector at the Large Hadron Collider (LHC). These measurements reflect 800 mu b(-1) of data taken during 2010. Jets are reconstructed using the anti-k(t) algorithm with radius parameter R varying between 0.2 and 1.0. Distributions of the charged-particle multiplicity, the scalar sum of the transverse momentum of charged particles, and the average charged-particle p(T) are measured as functions of p(T)(jet) in regions transverse to and opposite the leading jet for 4 GeV < p(T)(jet) < 100 GeV. In addition, the R dependence of the mean values of these observables is studied. In the transverse region, both the multiplicity and the scalar sum of the transverse momentum at fixed p(T)(jet) vary significantly with R, while the average charged- particle transverse momentum has a minimal dependence on R. Predictions from several Monte Carlo tunes have been compared to the data; the predictions from Pythia 6, based on tunes that have been determined using LHC data, show reasonable agreement with the data, including the dependence on R. Comparisons with other generators indicate that additional tuning of soft-QCD parameters is necessary for these generators. The measurements presented here provide a testing ground for further development of the Monte Carlo models.