
finding the value of x
An open rectangular tank of height h metres with a square base of side x metres is to be constructed so that it has a capacity of 500 cubic metres. Prove that the surface area of the four walls and the base will be
2000 + x2 (the 2 is squared)
x
square metres. Find the value of x for this expression to be a minimum.
i have no idea where to even start on this one.

Are you saying it's equal to.........
$\displaystyle 2000 + x^2$

that just how the question was written, and like i say i have no idea

Oh right I see now.
Volume of the tank = 500
Volume = $\displaystyle x^{2}h$
Thus
$\displaystyle h = \frac{500}{x^2}$
Surface area minus lid = $\displaystyle 4hx + x^2$
Substitute $\displaystyle h = \frac{500}{x^2}$ into surface area equation to get.
$\displaystyle 4\times\frac{500}{x^2}x + x^2 = S$
Where S is the surface area of the tank base and four walls.
This simplifies to be
$\displaystyle \frac{2000}{x} + x^2 = S$
Happy new year.
Regards,
Ross

would it not be 5x instead of 4x on this bit
http://www.mathhelpforum.com/mathhe...29200f481.gif
as there are 4 sides and a base so altogether 5 surfaces.?

No, because it's 4 walls are the same surface area but not the base.
Thus the base is still the $\displaystyle x^2$ and the four walls are represented by the other component.
