A rectangular box is to have a square base and a volume of 10 ft$^3$. The material for the base costs 29 cents/ft$^2$, the material for the top costs 23 cents/ft$^2$, and the material for the sides costs 18 cents/ft$^2$. If $x$ denotes the length of one side of the base (in feet), find a function in the variable $x$ giving the total cost of materials used in constructing the box in cents.
$\bigcirc \ 52x^2 + \frac{720}{x}$
$\bigcirc \ 52x^2 + \frac{180}{x}$
$\bigcirc \ 52x^2 + \frac{180}{x^2}$
$\bigcirc \ 52x^2 + \frac{72}{x}$
$\bigcirc \ 52x^2 + \frac{720}{x^2}$
What is the domain of the function?
$\bigcirc \ (0, 10)$
$\bigcirc \ (1, 10)$
$\bigcirc \ (-\infty, 0) \cup \ (0, \infty)$
$\bigcirc \ (0, \infty)$
$\bigcirc \ (-\infty, \infty)$