The PHENIX experiment has measured midrapidity transverse momentum spectra (0.4 < p(T)<4.0 GeV/c) of single electrons as a function of centrality in Au+Au collisions at roots(NN) = 200 GeV. Contributions from photon conversions and Dalitz decays of light neutral mesons are measured by introducing a thin (1.7% X-0) converter into the PHENIX acceptance and are statistically removed. The subtracted nonphotonic electron spectra are primarily due to the semileptonic decays of hadrons containing heavy quarks, mainly charm at lower p(T). For all centralities, the charm production cross section is found to scale with the nuclear overlap function, T-AA. For minimum-bias collisions the charm cross section per binary collision is N-c (c) over bar/T-AA=622+/-57(stat)+/-160(syst) mu b.