# Math Help - open-topped box promblem?

1. ## open-topped box promblem?

Not sure how to do this problem if anyone could show me how it would be greatly appreciated. An open-topped box with square base is to be built for $48. The sides of the box will cost$3 per square meter, and the bottom of the box will cost $12 per square meter. If the edge-length of the square base is "x", express the VOLUME V of the box as a function of "x"? V=__x^3__x^2__x 2. The question, as you have stated it, makes no sense. First, there is no "figure to the right". Also you refer to costs for top, sides, and bottom but there is no reason to think that would have anything to do with the volume of the box. If there is a condition, such as making the box as inexpensive as possible, it would be a good idea to mention it! 3. Originally Posted by The Math Man Not sure how to do this problem if anyone could show me how it would be greatly appreciated. An open-topped box with square base (as in the figure at the right) is to be built for$48. The sides of the box will cost $3 per square meter, and the bottom of the box will cost$12 per square meter. If the edge-length of the square base is "x", express the VOLUME V of the box as a function of "x" by entering integers below (such as 7, 0, or -4). Hint: use the first two sentences to express the height of the box in terms of "x".
The box has a square base with sides of length $x,$ and a height which we will call $h\text.$ Then you should know that the volume of the box is $V=x^2h\text.$ In order to get this in terms of just $x,$ we need to find a relationship between $x$ and $h\text.$

We know that the box should cost exactly $48. The cost of the base is $\12x^2$ ($12 per square meter), and the cost of the sides of the box will be $\3\cdot4\cdot hx = \12hx$ (multiplying by 4 since there are four sides). Since the total is $48, we have $48 = 12x^2 + 12hx\text.$ Now you can solve for $h$ and substitute back into the volume equation. 4. Originally Posted by The Math Man Not sure how to do this problem if anyone could show me how it would be greatly appreciated. An open-topped box with square base is to be built for$48. The sides of the box will cost $3 per square meter, and the bottom of the box will cost$12 per square meter. If the edge-length of the square base is "x", express the VOLUME V of the box as a function of "x"? V=__x^3__x^2__x
Assign variables
$
x =$
side of the base
$h =$ height of the box
$c=$ cost

apply the necessary formula

$c=12+3*h$

$c=12x^2+3(4x)h$

$c=12x^2+12xh$

total cost =48$thus $48 = 12x^2 + 12xh$ $48 - 12x^2 = 12xh$ $h = \frac{48 - 12x^2}{12x}$ $h = \frac{4}{x} - x$ $V = x^2h$ $\boxed{V = x^2 (\frac{4}{x} - x)}$ 5. My apologies math man, I missed the part where the box was to cost$48.