A closed box with a square base is to have a volume of $10,125c{m}^3.$ The material for the top and bottom of the box costs $$4\mathrm{.}50$ per square centimeter, while the material for the sides costs $$1\mathrm{.}50$ per square centimeter. Find the dimensions of the box that will lead to the minimum total cost. What is the minimum total cost

Write an equation for $C(x),$ the cost of the box as a function of $x,$ the length of a side of the base.

$C(x)=$