Hi,

I just started taking a Pre-Calculus math course in College. I took this course years ago and since then have forgotten most of what I have learned. I have come across the following question which I am stuck on.

A box with a square base has a volume of 600 cubic cm. If the material for the 4 sides and the top costs 5 cents per square cm and the material for the reinforced base costs 10 cents per square cm, express the total cost C of material (in cents) as a function of x, where x is the length of a side of the square base. Write the function in simplified form.

I have gotten this far:

$\displaystyle 600 = w^2*h$

$\displaystyle h = 600/w^2$

Area = $\displaystyle 2w^2 + 4*w(600/w^2)$

Area = $\displaystyle 2w^2 + 2400/w$

The answer that is given to me is $\displaystyle C(x) = 15x^2 + 12000/x$

I can see that if I multiply the 2400 by 5 I will get the $\displaystyle 12000/x$ but I don't understand where the $\displaystyle 15x^2$ comes from.