Q$3.$ Finding surface area of a potato using thermocouple!

You claim to calculate surface area of a potato using lumped capacitance model. A

potato has a specific heat of $3\mathrm{.}64k\frac{J}{k}g*K,$ density of $1055k\frac{g}{m^3}.$ and thermal

conductivity of $0\mathrm{.}498\frac{W}{m}.k.$ You measure mass of a potato to be $0\mathrm{.}175$ kg and put in an

oven at a temperature of $200C.$ Within four minutes temperature of the potato rises from

$25C$ to $50C.$ Assuming an overage heat transfer coefficient of $h=15\frac{W}{m^2}K$ in the

oven, what is the sufface area of the potato? Is your approoch accurate? $(35$ points$)$