A box that has a lid, "floor" that is a square with sides x, and hight is h, has a surface area of 384 dm^{2 }
How does this equation show the volume of said box?
V(x)=(x(192-x^{2}))/2
The surface area of the box in square decimeters is:
$\displaystyle 384=2x^2+4xh$ and so solving for $\displaystyle h$ we find:
$\displaystyle h=\frac{384-2x^2}{4x}=\frac{192-x^2}{2x}$
The volume is then:
$\displaystyle V=x^2h=x^2\left(\frac{192-x^2}{2x} \right)=\frac{x(192-x^2)}{2}$