Thread: Finding Volume of a Box

Im a little confused with this problem:




A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting 3 cm squares from each corner and folding up the sides. Let x represent the width of the original piece of cardboard. Find the width of the original piece of cardboard, x, if the volume of the box is 3300 cm squared.

---


I think this is how you set up the equation, but im having trouble factoring it out in the end.. so im not sure if I have it set up right.

(6)(2x-6)(x-6)= 3300

Where is the initial 6 coming from?

3+3 to get the height ? am i not supposed to do that with this problem ?

wait.. i dont know why I did that. Am i supposed to just divide the 3300 by 3?


so it would be

(3)(2x-6)(x-6)=3300?

yes, your reasoning is correct. Now we foil:





Now we divide by 6:







x must be 28, since a negative value is not possible.

Hello, Jerry99!

The cardboard looks like this:

Code:

      : - - - - 2x- - - - - :
    - *---*-----------*---* -
    : |///:           :///| 3
    : * - *-----------* - * -
    : |   |           |   | :
    x |   |           |   | x-6
    : |   |           |   | :
    : * - *-----------* - | -
    : |///:           :///| 3
    - *---*-----------* - * -
      : 3 : -  2x-6 - : 3 :

The box looks like this:

Code:

          *-----------*
         /|          /|
        / * - - - - / *
       / /         / /
      *-----------* / x-6
    3 |           |/
      *-----------*
           2x-6

The volume is 3300 cm

So we have: .

. . which simplfies to: .

. . which factors: .

. . and has the positive root: .

thanks for the help guys