Come up with the best container to hold M&M's...

[wviperw]

This is a math project that we get to do in Pre-Calculus. Sounds fun doesn't it? What I have to do is, from a peice of poster board, make a container to hold the maximum amount of M&M's for a shipping company. It should also be easy to assemble and collapse (or something like that). I also have to come up with equations and stuff like that. My teacher said that I was allowed to have as many outside sources as I want. I am hoping you guys are somewhat smart...

Rules:
1. 22 x 30 in posterboard
2. Allowed to cut it, allowed to have tape (but not to add surface area)
3. Must be completely closed (except a door which will open and shut to put M&M's in
4. Math Calculations need to be with no more then 1% errancy

So what shape would be best? Originally I thought a cube would be best, but then shapes such as spheres came popping in my head.

 

[NikPreviousAcct]

...but a sphere wouldn't be practical for a shipping company... right??

 

[Czar]

A box with rounded corners.

 

[Regine]

But if you make rounded corners, wouldn't that leave less volume for the m&m's?

I'd say a big cube, with a little flap cut in the top as a little door.
Try some calculations first to see which would give you more volume.

 

[Czar]

True that you would get less space with rounded corners but the space you would have would be better used. You have to take into count that you have to minimese the space between the m&M, and because the m&m are rounded then where they come in contact with the box it would be best to have that rounded as well.

 

[NikPreviousAcct]

cut the cardboard into eight small boxes, all containing powerul magnets. Design it so that the magnets keep the eight boxes hover at eight points in the air, making a cube. Then, as you toss M&M's between the eight small boxes, the magnetic field holds them in place there.

Voila.


More space for M&M's than you could have imagined.





brought to you today by the letters "bs," and also by the number idea "0%".

 

[wviperw]

Yea, I don't think a sphere would fold up too easily...

 

[jhu]

a cd jewel case

 

[G41184b]

The more sides something has the more area/ volume it contains, so something like an octagon [if possible to fold] would hould more m&m's than an cube, try to find the best combination of number of sides and practicality. I would try something like a hexagonal prism, the bottom and tops hexagons and the sides rectangles. Good luck

 

[GammaRayX]

Does the box have to be in one piece when folded, or you can have as many peices as you wish?

If it must be in one piece, then you are going to run into some problems and limits your design.

But at any rate, if you can have as many peices as you wish, then get it as close to a sphere as possible. Since a sphere have the highest volume to surface area ratio.

For example, a tetrahedron is a start, a cube is better, an octahedron is even better, and a dodecahedron (12 sides) is even better, and isohedron (20 sides) is even better. And even better, for regular shapes, theres formulas avaible and you can easily get to that accurate 1% requirement. Another shape that consists of pentagons and hexagons is a soccerball (IIRC 60 sides) and its the same shape as buckeyballs (new form of carbon).

Off the top of my head, a dodecahhedron have 12 sides. Each side consists of a pentagon (5 sided polygon) connected to each other. You can maximize the amount of the posterboard used be figuring out a repeating patern you can use for the board and how to get the most out of the "edges" of the board.

 

[ratkil]

Give me a break, my digestive system will hold more than any container you are going to come up with. You never said they had to remain in their natural state.......

 

[HigherGround]

how about my mouth, gimme all your M&Ms and i'll hold them for you

 

[wviperw]

Thanks for all the help.

GammaRayX, the box can be in different pieces but they would be taped. Thanks for the different ideas.

I was thinking that maybe I could split the poster board into 2 seperate sheets of 22 x 30. Would this be plausible since poster board is a little thicker than paper?

 

[Shalmanese]

There is also the matter of how much cardboard you are wasting in the end. The best bet(if you can be bothered) is to go for a icosododecahedron or whatever it's called if you can be bothered. Basically its about 96 equilateral trianges making a big ball shape. This would probably be your best cahnce but the maths would be p pain in the ass to work out... especially to 1 %. your next best bet would to be a rectangular prism given the dimensions of the cardboard. If you wnated to be really iniative and piss the teacher off, grind up the cardboard into a powder/ granules, get a big balloon or any round thing and paper maiche it on. Make sure you get a spherical object so you can work out the maths easily.

 

[Shalmanese]

There is also the matter of how much cardboard you are wasting in the end. The best bet(if you can be bothered) is to go for a icosododecahedron or whatever it's called if you can be bothered. Basically its about 96 equilateral trianges making a big ball shape. This would probably be your best cahnce but the maths would be p pain in the ass to work out... especially to 1 %. your next best bet would to be a rectangular prism given the dimensions of the cardboard. If you wnated to be really iniative and piss the teacher off, grind up the cardboard into a powder/ granules, get a big balloon or any round thing and paper maiche it on. Make sure you get a spherical object so you can work out the maths easily.

 

[wviperw]

ya I was thinking about paper mache but I don't think that is feasible. How would you calculate a baloon shape? or even if it was somewhat sperical it wouldn't be too precise

 

[Ornery]

Think cylindrical, like a mailing tube. Roll into such a size that you have just enough left to make the top and bottom.

Or think about making a box that wastes the least amount of that 22" x 30" cardboard. Whatever cardboard ends up on the floor means that much fewer M&Ms contents.

 

[Ornery]

I've got an Acad Drawing Desktop Shot, but I can't figure out how to get the whole thing copied.

Basically, the 30" side is divided or folded at 2.66", 2.66", 11", 2.66" then 11". The bottom 2.66" x 22" piece is divided in half and used as top and bottom. No waste!

Drawing2

 

[Mday]

if not allowed to be round, a cube would maximize volume and surface area, otherwise, sphere.

do you know calculus?

anyway...

i don't want to be bothered....

 

[lestat]

mday he is in precal, i think its safe to assume he does not know calculus =[ unless he is calculon from futurama...

 

[minus1969]

Ornery's got it...round the posterboard to form a cylinder and make cones out of the ends. To collapse, untape, unroll, and fold however you like. BAM! an A .

 

[MI6]

A sphere is the best bet (but will it be collapsable?) What about a half a cone. One corner to a point then play around with the biggest base with the talles cone. This is a real calc problem. Find the equations for a cone then do a related rate problem.

Another thought would be to take a full cone and put them base to base (not point to point). Don't have to worry about the base to hieght stuff and really easy to play with.

 

[Opinionated]

Took a minute and through this one together for you...

Surface area 660 sq. in (0% materials waste).
Volume = 1125 cu. in.
Meets minimum requirements and is a fair tradeoff between volume and difficulty in manufacture, packaging and shipping unassembled packages in bulk, storage, etc....

Here's a link to an image I through together. Has the die layout... sorry, no time to do the 3D solid drawings.... It is essentially a box with a smaller "box" attached on top.

Diagram and Description of an M&M Box

Hope this helps. You CAN of course get more volume from the same material, but it progressively moves away from the "ease of use" and the math gets much more difficult.

Opinionated

 

[Opinionated]

wviperw - Did you look at my suggestion?

Has anyone been able to come up with a better one?

Opinionated

 

[Demon-Xanth]

Best way to hold Eminem: Small air tight container, preferably with shards of broken glass

Edit: Whoops, wrong M&M