A styrofoam cooler $($K $=\mathrm{.}030$ W$/$mo C$)$ has outside dimensions of $0\mathrm{.}130$ m x $0\mathrm{.}330$ m x $0\mathrm{.}420$ m$,$ and an average thickness of $2\mathrm{.}2$ cm$.$ About how long will it take for $4\mathrm{.}10$ kg of ice at $0$o to melt in the cooler if the outside temperature is $22\mathrm{.}0$o$?$