A nickel coin with initial temperature $Ti=310K$ falls into a cold lake with temperature $T_{}$

$=275K.$ The heat transfer coefficient $h=200\frac{W}{m^2}K.$ For nickel alloy: $Cp=3\mathrm{.}8M\frac{J}{?}$

$m^{3}K$ and $k=15\frac{W}{m}K.$ The diameter of the nickel is $20$ mm and the thickness is $1\mathrm{.}25$ mm $.$

$($a$)$ Sketch the time dependence of the coin temperature. $($b$)$ How long does it take for the

coin to reach $280$ K $?$