Calculate Dimensions of Box SpongeBob Square Pants to Make Volume > 100cm^3

[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

 

[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

 

[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

 

[Integral]

https://www.physicsforums.com/showthread.php?t=132871" may have some useful information for you. Read it then see if you get any ideas.

 

[thomasrules]

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

 

[thomasrules]

$$2x+y = 30$$

$$2x+z = 30$$

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

?

 

[Integral]

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

 

[thomasrules]

yea $$xyz > 100$$

 

[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?

 

[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?

$V=\ldots$ ?

 

[Integral]

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.

 

[benorin]

Box => use diagram :)

Consider the diagram:

http://123pichosting.com/thumbs/3498Dimensions of Box.JPG

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...

 

[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?

 

[HallsofIvy]

I've merged the three threads.