# Thread: Does this equation describe the volume of the box?

1. ## Does this equation describe the volume of the box?

A box that has a lid, "floor" that is a square with sides x, and hight is h, has a surface area of 384 dm2

How does this equation show the volume of said box?
V(x)=(x(192-x2))/2

2. ## Re: Does this equation describe the volume of the box?

The surface area of the box in square decimeters is:

$384=2x^2+4xh$ and so solving for $h$ we find:

$h=\frac{384-2x^2}{4x}=\frac{192-x^2}{2x}$

The volume is then:

$V=x^2h=x^2\left(\frac{192-x^2}{2x} \right)=\frac{x(192-x^2)}{2}$