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We want to construct a rectangular parallelepiped with Volume $2L$, one of its sides measures $10$cm, let $x$ and $y$ be the two dimensions in dm, of this box. (Note: $1$dm = $10$cm)

1)Prove that the surface of this box is $S(x) = 2x+4+4/x$.

2)What are the dimensions such that the quantity of matter used to fabricate it is minimal?

I think I misunderstood something; the given isn't really clear. Can I get some help?

Benjamin Wang
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Iridium
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1 Answers1

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One of the sides is $10$ cm i.e $1$ dm (decimeter). Other two sides are $x$ and $y$ dm.

So volume of box $V = 2 = xy \implies y = \frac{2}{x}$

Surface area $S = 2(xy + y + x)$ (as one of the sides is $1$).

Writing $y$ in terms of $x$,

$S = 4 + 2x + \frac{4}{x}$.

Now to find $x$ that minimizes the surface area, differentiate $S$ with respect to $x$ and equate to zero.

Can you take it from here?

Math Lover
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