When an air bubble rises from the bottom to the top of a freshwater lake, its volume increases by $82\%.$ If the temperatures at the bottom and the top of the lake are $5\mathrm{.}6$ and $20\backslash$deg C$,$ respectively, how deep $($in m$)$ is the lake? $($Assume the density of water is $1\mathrm{.}000\backslash$times $103$ kg$/$m $3.)$