Secondary beams of 3He, 4He, 6He, and 8He were produced through the projectile fragmentation of an 800 MeV/nucleon 11B primary beam. Interaction cross sections (σI) of all He isotopes of 790 MeV/nucleon on Be, C, and Al targets were measured by a transmission-type experiment. The interaction nuclear radii of He isotopes RI(He) = (σIπ)12 − R I(T) where RI(T) is the radius of the target nucleus, have been deduced to be RI(3He) = 1.59 ± 0.06 fm, RI(4He) = 1.40 ± 0.05 fm, RI(6He) = 2.21 ± 0.06 fm, and RI(8He) = 2.52 ± 0.06 fm.