Max Volume Suitcase Homework: Solving Max/Min Problems

  • Thread starter Thread starter Punkyc7
  • Start date Start date
  • Tags Tags
    Max
Click For Summary

Homework Help Overview

The problem involves creating a suitcase with maximal volume by folding and cutting square corners from a standard 8.5 by 11 inch sheet of paper. Participants are exploring the relationship between the dimensions of the box and the volume, as well as the folding process required to construct the box.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the dimensions and volume calculations, questioning the necessity of surface area in the context. There are attempts to clarify how to properly fold the paper to create a closed box, with some uncertainty about whether the box should have a lid.

Discussion Status

The discussion is ongoing, with participants providing insights into the folding process and questioning the original poster's approach. There is a mix of interpretations regarding the box's design, particularly whether it should be open or closed, and guidance is being sought on the correct method to achieve the desired shape.

Contextual Notes

Some participants express confusion about the folding technique and the implications of cutting square corners, indicating a need for visual aids to clarify the construction process. There is also a mention of the requirement for a lid, which adds complexity to the problem.

Punkyc7
Messages
415
Reaction score
0

Homework Statement


The object is to fold and then cut square corners from a standard 8.5 by 11 inch sheet of paper to create a suitcase of maximal volume


Homework Equations


V=L*W*H
SA=2LW+2LH+2WH


The Attempt at a Solution


93.5=2(8.5-2x)(11-2x)+2(11-2x)2x+2(2x)(8.5-2x)
x=1.375

then i plugg it into the Volume equation my lenghts are
(8.5-2(1.375))=5.75
(11-2(1.375))=8.25
1.375=1.375

Then i try to build it out of a piece of paper and it doesn’t close like it is suppose too, can anyone figure out where I went wrong it would be greatly appreciated
 
Physics news on Phys.org
What does surface area have to do with this problem? And how do you fold and then cut corners out? And how do you fold it to make a suitcase with the corners missing?

Please state the problem, word for word, from your text, along with any pictures they give.
 
That was word for word. I am not sure if you needed the surface area i was just trying to solve for x since there is only so much paper. So you have a piece of paper an you have to cut the corners out to construct a box with the maximum volume inclosed. So their must be a lid on the box so its like a suitcase.
 
It's not closing because you're making an open box from what I can see.

I assume x means the height and this is the type of box you're supposed to be creating (I'm unsure if this design will make for max volume though):

http://img30.imageshack.us/img30/654/boxlayout.png

where a=8.5, b=11

So 8.5-2h=w
and 11-2h=2l while it looks like you made it 11-2h=l
 
Last edited by a moderator:
Punkyc7 said:
That was word for word. I am not sure if you needed the surface area i was just trying to solve for x since there is only so much paper. So you have a piece of paper an you have to cut the corners out to construct a box with the maximum volume inclosed. So their must be a lid on the box so its like a suitcase.

You can make an open top box by folding up the flaps after cutting square corners out of the paper. I have no idea how to fold it to make a closed container. Are you certain the box is to be closed? You can still calculate the volume a box would hold even if it doesn't have a top.
 
LCKurtz said:
You can make an open top box by folding up the flaps after cutting square corners out of the paper. I have no idea how to fold it to make a closed container. Are you certain the box is to be closed? You can still calculate the volume a box would hold even if it doesn't have a top.

yea the box must have a top
 
Punkyc7 said:
yea the box must have a top

Please supply a picture of how you cut square corners out of a sheet of paper then fold it to make a closed rectangular box. I don't see how you do that and you can't work the problem without knowing how it is folded.
 
LCKurtz said:
Please supply a picture...
And is my picture just for decoration?
 
Mentallic said:
And is my picture just for decoration?

Your picture does not show cutting square corners from the sheet as the OP requires. I can't speak to how decorative it is. :smile:
 
  • #10
Yea, as I read it, its an open topped box from the fact that the corners cut out must be square. Presumably you will make the lid separately, or travel with all your stuff open to the elements.
 
  • #11
LCKurtz said:
Your picture does not show cutting square corners from the sheet as the OP requires. I can't speak to how decorative it is. :smile:

Oh gosh you're right! Actually... *attempts to cover mistake ingeniously*.. I assumed square corners implied rectangles :biggrin:

In that case, I second post #2. How do you do it?
 

Similar threads

Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
7
Views
2K
Replies
3
Views
2K
Replies
7
Views
3K
Replies
3
Views
2K
  • · Replies 23 ·
Replies
23
Views
7K
Replies
3
Views
7K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
7K