# Thread: Finding Volume of a Box

1. ## 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.

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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

2. Where is the initial 6 coming from?

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

4. 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?

5. yes, your reasoning is correct. Now we foil:

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

$3(2x^2-18x+36)=3300$

$6x^2-48x+108=3300$ Now we divide by 6:

$x^2-9x+18=550$

$x^2-9x-532=0$

$(x-28)(x+19)=0$

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

6. Hello, Jerry99!

$\text{A piece of cardboard is twice as long as it is wide.}$
$\text{It is to be made into a box with an o{p}en top}$
$\text{by cutting 3 cm squares from each corner and folding up the sides.}$

$\text{Let }x\text{ represent the width of the original piece of cardboard.}$

$\text{Find the width of the original piece of cardboard }x,$
$\text{if the volume of the box is 3300 cm}^3.$

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 $^3.$

So we have: . $3(2x-6)(x-6) \:=\:3300$

. . which simplfies to: . $x^2 - 9x - 532 \:=\:0$

. . which factors: . $(x - 28)(x + 19) \:=\:0$

. . and has the positive root: . $x \:=\:28\text{ cm.}$

7. thanks for the help guys