The differential cross sections of the inelastic α + 12C scattering leading to the excitation of the short-lived 2 2 + (E x = 9.84 or 9.6 MeV) state in 12C have been analysed within a modified diffraction model. We determined the diffraction radii of 12C in this excited state at E α = 386 and 240 MeV and compared them with the diffraction radius for the 0 2 + (E x = 7.65 MeV) Hoyle state. We found that the rms radii for the 2 2 + state is 〈R(2 2 + )〉 = 3.07 ± 0.13fm, which agrees well with the rms radius of the 0 2 + , 7.65 MeV Hoyle state and is a factor of 1.3 larger than the rms radius for the ground state of 12C. The similarity between the rms radii of the 0 2 + and 2 2 + states provides a strong argument in favor of a hypothesis that the 2 2 + state is the first member of a rotational band based on the 0 2 + Hoyle state.