We extract the freezeout hypersurface in Pb-Pb collisions at $sqrt{s_{rm NN}}=$ 2760 GeV at the CERN Large Hadron Collider by analysing the data on transverse momentum spectra within a unified model for chemical and kinetic freezeout. The study has been done within two different schemes of freezeout, single freezeout where all the hadrons freezeout together versus double freezeout where those hadrons with non-zero strangeness content have different freezeout parameters compared to the non-strange ones. We demonstrate that the data is better described within the latter scenario. We obtain a strange freezeout hypersurface which is smaller in volume and hotter compared to the non-strange freezeout hypersurface for all centralities with a reduction in $chi^2/N_{df}$ around $40%$. We observe from the extracted parameters that the ratio of the transverse size to the freezeout proper time is invariant under expansion from the strange to the non-strange freezeout surfaces across all centralities. Moreover, except for the most peripheral bins, the ratio of the non-strange and strange freezeout proper times is close to $1.3$.
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