Pre-calculus question help

[watchthesky30]

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions W inches by L inches by cutting out equal squares of side x at each corner and then folding up the sides. (W = 12 in. and L = 20 in).

http://www.webassign.net/scolalg5/3-FoM-26.gif

(b) Find the values of x for which the volume is greater than 200 in3. (Give each answer correct to three decimal places.)

[ ] < x < [ ]

(c) Find the largest volume that such a box can have. (Round your answer to three decimal places.)
[ ] in^3


Can somebody please help me with this? I don't understand this :?:
If you could show me steps on how to do these questions, that would be great incase something like this appears on my midterm. But any help would be nice .

 

[DrMike]

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions W inches by L inches by cutting out equal squares of side x at each corner and then folding up the sides. (W = 12 in. and L = 20 in).

http://www.webassign.net/scolalg5/3-FoM-26.gif

(b) Find the values of x for which the volume is greater than 200 in3. (Give each answer correct to three decimal places.)

[ ] < x < [ ]

(c) Find the largest volume that such a box can have. (Round your answer to three decimal places.)
[ ] in^3


Can somebody please help me with this? I don't understand this :?:
If you could show me steps on how to do these questions, that would be great incase something like this appears on my midterm. But any help would be nice .

Ok, what is the height of the box? And the width? And the length?

The height is easy : it's x. The width will be a formula involving W and x, likewise, the length will involve L and x.

Now, you "know" the width, length and height - at least, you know them as formulas involving x. So, what is the volume of the box? Again, this will be a formula V(x) involving x.

Then, the two questions are :

* find x such that V(x)>200
* find x such that V(x) is as big as possible.