If 1100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Question

anonymous · Answer

got a picture?

anonymous · Answer

if you call the lenght of the base $x$ and the height $h$ then the base has area $x^2$ and the four sides have area $xh$ making the total 
$$x^2+4xh$$

anonymous · Answer

since you know that total is $1100$ you can set $$x^2+4xh=1100$$ and solve for $h$ in terms of $x$

anonymous · Answer

pretty much in your head
i get 
$$h=\frac{1100-x^2}{x}$$

anonymous · Answer

then the volume is 
$$V=x^2h$$ but now it is 
$$V(x)=x^2(\frac{1100-x^2}{x})$$ maximize that one

anonymous · Answer

you good from there?