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

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- Oct 30th 2012, 08:30 AMGardsVisionDoes 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 dm

^{2 }

How does this equation show the volume of said box?

V(x)=(x(192-x^{2}))/2 - Oct 30th 2012, 09:06 AMMarkFLRe: Does this equation describe the volume of the box?
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:

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