What is the maximum volume possible from a piece of cardboard that is made into a cube, that measures 16 inches by 12 inches?

[___________ ]
[ __________ ]
[___________ ] 12 - 2x
[____________]
16in - 2x

• A Box with no top.

$\displaystyle L = 12-2x$
$\displaystyle W = 16 - 2x$
$\displaystyle n = x$

$\displaystyle V = 172 - 32x - 24x + 4x^2(x)$

$\displaystyle V = 172x - 32x^2 - 24x^2 + 4x^2$

$\displaystyle 4x^3 - 24x^2 - 32x^2 + 172x$

$\displaystyle 4x^3 - 56x^2 +172x$

$\displaystyle 4x(x^2 - 14x + 43)$
$\displaystyle How to solve for X.$

this is where I got stuck.

Thank you

2. Originally Posted by The D00D
Note: One with x#'s, are exponents, since I don't know to do an exponent on here

Thank you
Use ^ (it's <shift>6 on most keyboards) so x^2 becomes $\displaystyle x^2$.

3. Thank you for that.

4. Okay so I've been looking at this question and I'm not sure I understand what it's asking, so I'm not sure how you got your initial equations.

But given your starting equations, I rather think you'll find that in your first step, 12 x 16 is a little bit more than 172.

Your end equation should be something like
$\displaystyle 4x (x^2 - 14x + 48)$