$(20$ POINTS$)$ Problem Statement: A $6-$cm$-$diameter $13-$cm$-$high canned drink initially at $25C$ is to be cooled to $5C$ by dropping it into iced water at $0C.$ The total surface area and volume of the can are $A=301\mathrm{.}6c{m}^2$ and $V=367\mathrm{.}6c{m}^3.$ If the heat transfer coefficient is $120\frac{W}{m^2*C},$ determine how long it will take for the drink to cool to $5C.$ Assume the can is agitated in water and thus the temperature of the drink changes uniformly with time. Properties: $k=0\mathrm{.}607\frac{W}{m*C},c_p=4180\frac{J}{kg*C},=977k\frac{g}{m^3}$

$D=\mathrm{.}06rs$

$tc=25C-7c^{001}cbSC$

height $=\mathrm{.}13m$