Does this equation describe the volume of the box?

**GardsVision** · October 30th 2012, 08:30 AM

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

**MarkFL** · October 30th 2012, 09:06 AM

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:

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

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