A Closed box with a square base must have a volume of 10 cubic feet. Express the amount A of material used to make such a box as a function of the length x of a side of the square base.

Question

anonymous · Answer

and then i bet we are going to find the least amount of material.
put x = length of bottom edge so area of base is 
$$x^2$$ since it is a square and area of top is also 
$$x^2$$ since the box is closed.  if the height of the box is say "h" then the volume of the box is 
$$x^2h$$ but since you know that the box contains 10 cubic feet, this tells you that 
$$x^2h=10$$ so 
$$h=\frac{10}{x^2}$$

anonymous · Answer

we have two squares both with side x to that takes 
$$2x^2$$ of material.  then we have 4 sides with area $$xh$$ so that takes 
$$4xh$$ material for a total of 
$$2x^2+4xh$$ material.  now replace h by 
$$\frac{10}{x^2}$$ and we get 
$$A(x)=2x^2+\frac{40}{x}$$  if my algebra is correct