In this work, we use a spherical shell with an attractive potential to simulate the C<sub>60</sub> and its effects on, He, Ne, Ar and Kr when each atom is in the center of the sphere. Within the Kohn-Sham model, two exchange-correlation functionals were used; the main difference between these two functionals is that one incorporates explicitly the self-interaction correction and the correct asymptotic behavior of the exchange-correlation potential, and the other one does not contain such corrections. We found that the considered atoms are softer inside of the cage than when they are free. By using several chemical reactivity predictors as the electrodonating and electroaccepting powers, defined by Professor Gázquez <em>et al</em>. (<em>J. Phys. Chem. A</em> 2007, <em>111</em>, 1966), it is proved that the noble gases increase their chemical reactivity when they are immersed in the C<sub>60</sub>. Naturally, this conjecture must be confirmed by more realistic models, but at first glance this is a very interesting conclusion and opens a new possibility to obtain reactions with encaged inert gases.