Question

A rectangular box is to have a square base and a volume of 70 ft3. The material for the base costs 38¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 27¢/ft2. Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.

Answer 1

$x-length\ of\ one\ side\ of\ base\\y-high\ of\ box\\x^2-area\ of\ base\\x^2y-volume\\\\x^2y=70\\y=\frac{70}{x^2}\ \ \ \ \ \ \ \ and\ x\neq0\\\\38x^2+4\cdot10xy+27x^2\\65x^2+40xy\ in\ cents\\\\0.65x^2+0.4xy\ in\ dollars$