Question 1045809
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Let *[tex \Large s] be the measure of the side of the base and let *[tex \Large h] be the height.


The volume of the box is *[tex \Large V\ =\ hs^2\ =\ 16823], so *[tex \Large s\ =\ \sqrt{\frac{16823}{h}}]


The total surface area of a such a box is *[tex \Large S\ =\ s^2\ +\ 4sh], but substitute for s from above:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  S(h)\ = \frac{16823}{h}\ +\ 4h\sqrt{\frac{16823}{h}}]


Find *[tex \Large \frac{dS}{dh}], set it equal to zero, and solve.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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