Maximixe the voliume of a box

Goistein

Junior Member
Joined
Oct 8, 2006
Messages
109
I need to make a topless box and maximize the voliume. To do this I have a 20x28cm piece of paper. I cut off four corners, but they must all be squares of the same size. Then It looks like this:
Code:
   +----------+
   |          |
+--+          +--+
|                |
+--+          +--+
   |          |
   +----------+
(Hope fully, the spaces show up)
Fold the four side rectangles, to make a box wiht no top. What are the dimensions of the square that I should cut out :?:

P. S. I managed to obtain a voliume of 960 cm by making the dimensions 4x4. But I know that the max is a little more than 961, with dimensions approxamatly 3.8. But I want an exact answer.

P.S.S. This might be pre calc, but the assignment is from Honors A2.
 
Goistein said:
I need to make a topless box and maximize the voliume. To do this I have a 20x28cm piece of paper. I cut off four corners, but they must all be squares of the same size....
Let x = side of square you make on each corner

Then, when you "fold" up the paper to make an open box,

length of box = 28 - 2x
width of box = 20 - 2x
height of box = x

Volume of box = (28 - 2x)(20 - 2x)(x)

Does that help? I did get ~3.8 inches for the length of the side of the square you cut out on each corner.
 
Yes, but I want to know how to maximize it. I graphed it on my calc, and found the max, but how to do that? But thanks for the answer Denis! I'm gonna win the class contest!

Whatever. Here're 2 cookies.
:):) I think I threw up.
:):) It's on fire!
I have more colors too!
 
Goistein said:
Yes, but I want to know how to maximize it.
Ok; we have:
Volume of box = (28 - 2x)(20 - 2x)(x)

Perform the multiplications; after simplification:
V = x^3 - 24x^2 + 140x

Set to 0; 1st derivative:
3x^2 - 48x + 140 = 0
Solve using quadratic:
x = 2 [12 +- sqrt(39)] / 3 : 12 + sqrt(39) is out of range, so:

x = 2 [12 - sqrt(39)] / 3
 
How do you obtain the derivitive/slope of a non line? Maybe a link would help, but note that I'm in A2, not calc so it might take a little explaining.

Did you like the cookies?

Also, who edited my first post to make a picture. I noticed the spaces didn't show up at first...
 
Goistein said:
I noticed the spaces didn't show up at first...
You have to put the thing in "code" tags, if you're wanting to force the spacing. And then, since the message-entry box is in proportional spacing, but the "coding" tags introduce fixed-width spacing, you have to preview, then edit, then preview, then edit, then preview, then edit, then....

But you'll get there eventually! :wink:

Eliz.
 
stapel said:
Goistein said:
I noticed the spaces didn't show up at first...
You have to put the thing in "code" tags, if you're wanting to force the spacing. And then, since the message-entry box is in proportional spacing, but the "coding" tags introduce fixed-width spacing, you have to preview, then edit, then preview, then edit, then preview, then edit, then....

But you'll get there eventually! :wink:
Save yourself some time: do it in Notepad and copy it into the message box.
 
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