How Long Will It Take for Ice to Melt in a Styrofoam Cooler?

[Sucks@Physics]

Homework Statement

A large styrofoam cooler has a surface area of 1.0m^2 and a thickness of 2.5cm. If 5.0kg of ice at 0C is stored inside and the outside temperature is a constant 35C, how long does it take for all the ice to melt? (Consider conduction only)

Homework Equations

kA(delta)T/d = Q/(delta)T

Q=mc(delta)T

The Attempt at a Solution

I tried (.042J/mxsxC)(1.0m^2)(35C)/.025m = 58.8j/s but I don't think that the change in temperature is correct.

But after getting that answer solve for Q=(5.0kg)(2100J/kgxC)(35C) = 367500J again i don't think the change in temperature is correct

Then divide 367000J/58.8j/s = 104.4 hours. which i know is incorrect

Help would be appreciated thanks

 

[rl.bhat]

The cube has 6 surfaces. So the area should be 6.0m^2.

 

[Sucks@Physics]

the total surface area is 1.0m^2. But I figured it out, I just needed to use the latent heat equation