Dimensions of Box

1. Sep 26, 2006

thomasrules

Sponge Bob Square Pants makes an open-topped box from a 30-cm by 30-cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square, to the nearest hundredth of a centimetre, so that the volume of the resulting box is more than $$100cm^3$$????

OK so its a cubic function, other than that no idea really. I thought what you could do was multiply $$30*30-4x^2 = Area of Box$$because the squares are cut equaly so yea but don't know what that does me any good

2. Sep 26, 2006

thomasrules

Sponge Bob Square Pants makes an open-topped box from a 30-cm by 30-cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square, to the nearest hundredth of a centimetre, so that the volume of the resulting box is more than $$100cm^3$$????

OK so its a cubic function, other than that no idea really. I thought what you could do was multiply $$30 * 30-4x^2 =$$Area of Box because the squares are cut equaly so yea but don't know what that does me any good

BTW how do you do multiplication in TEX

Last edited: Sep 26, 2006
3. Sep 26, 2006

thomasrules

Sponge Bob Square Pants makes an open-topped box from a 30-cm by 30-cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square, to the nearest hundredth of a centimetre, so that the volume of the resulting box is more than $$100cm^3$$????

OK so its a cubic function, other than that no idea really. I thought what you could do was multiply $$30 * 30-4x^2 =$$Area of Box because the squares are cut equaly so yea but don't know what that does me any good

BTW how do you do multiplication in tex

4. Sep 26, 2006

Integral

Staff Emeritus
This thread may have some useful information for you. Read it then see if you get any ideas.

5. Sep 26, 2006

thomasrules

OOPS made extra threads by accident, moderator delete these if ya can

6. Sep 26, 2006

thomasrules

$$2x+y = 30$$

$$2x+z = 30$$

$$(2x+y)(2x+z) = 900$$

???

Last edited: Sep 26, 2006
7. Sep 26, 2006

Integral

Staff Emeritus
Can you write an expression for the VOLUMN of the box?

8. Sep 26, 2006

thomasrules

yea $$xyz > 100$$

9. Sep 26, 2006

jpr0

re: multiplication in tex

If you want to put a multiplication sign, it's \times
If you want to put a dot, you can use \cdot

If I gave you a box whose dimension (in units of metres) were:

length = $l$
width = $w$
height = $h$

what would the volume of the resulting box be?

Last edited: Sep 26, 2006
10. Sep 26, 2006

jpr0

Thomas before you go writing out inequalities, first of all write down what the volume of a box is.

If I gave you a box whose dimensions (in units of metres) were:

length = $l$
width = $w$
height = $h$

what would the volume of the resulting box be?

$V=\ldots$ ?

11. Sep 26, 2006

Integral

Staff Emeritus
you now have 3 equation and 3 unknowns. (the first 2 in post #3 and the expression for volumn.

You can now, with some manipulation solve the system.

12. Sep 26, 2006

benorin

Box => use diagram :)

Consider the diagram:

Notice that the blue squares are the ones Sponge Bob cuts away, and that the resulting square base of the box has edge length 30cm - 2x so that the dimensions of the box when folded up are: x by (30cm - 2x) by (30cm - 2x). Try to go from here...

13. Sep 26, 2006

thomasrules

thanks a lot benorin that diagram really made sense clearly to me

Ok i get it now $$x(30-2x)^2 = volume$$

then find x right but how would I do that can I factor it?

14. Sep 27, 2006

HallsofIvy

Staff Emeritus