Registered: Nov 1999
Location: Kutztown, PA, USA
Posts: 106

help me! ok...we have this contest...we have a 12x18 sheet of paper and we have to make a shape that has the highest volume. I dunno to make the cylinder (i think the cylinder is the way to go) i dunno if i should make it wider or higher) we have to have all sides covered...no open spaces..i will check this tomorrow morning...please help...i wanna win pizza (this is not cheating, he said we could ask for help)

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Greg Moore
[email protected]

Registered: Sep 1999
Location: Texan in Calgary for a while
Posts: 1361

Hmmm,

Since it's 12x18, plug the appropriate #s in for the various volume equations. I don't remember what a cylinder was offhand, but a square is LxWxD, or s^3. 12x18=216, so
x^3=216....x=6
Therefore, a cube measuring 6" on each side would have a volume of 216. This is pretty good because it uses all of the paper.

Not sure if a cube is the best, but there's a start for you.

Save a slice of pizza for me

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James Hromadka
VisorCentral.com
Personal Website: http://www.Hromadka.com

Registered: Jan 2000
Location:
Posts: 23

A sphere is the shape holding the greatest volume with any given surface area. It will be hard to make a sphere, but if you could do it, there is no way to have more volume; that's why planets and stars are round, and why water forms into spheres when there's no gravity. If you really wanted to undertake that, I'd suggest cutting your paper into a whole bunch of equilateral triangles, and then fastening them all together into a sphere shape (ever seen the "dome" at Epcot Center?)

~CYMagic

Registered: Mar 2000
Location: Hermosa Beach, CA
Posts: 222

I agree with CYMagic. The sphere is definitely the way to go if you are allowed to cut the paper. The smaller the triangles are, the closer you can get to obtaining a sphere, hence getting the largest volume for a given surface area.

Of course, if you had to fold the paper like Origami, the cube might be the simplest and easiest.

Good luck!


PS - JHromadka, the volume of a cylinder is the area of the circle times the height. Just in case you still wanted to know

Registered: Nov 1999
Location: Kutztown, PA, USA
Posts: 106

i will try the Sphere...i hope this works. I will report back tonight on the findings and to tell you if we won the pizza party. Now i just have to figure out a way to find the volume of a sphere. I know how to find the volume of a sphere, but not our sphere...i dunno what it will look like

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Greg Moore
[email protected]

[This message has been edited by GregMoore (edited 03-23-2000).]

Registered: Nov 1999
Location: bright side of the moon.
Posts: 996

HEY! i love these sort of competitions. so i did some web searching and found 3 interesting sites...i think the last one will help the most as it shows you how to build paper geodesics.....
http://www.pbs.org/wnet/bucky/dome.html http://w3.one.net/~monkey/index.html - good one! http://www.dnaco.net/~michael/domes/others.html - shows how to make paper geodesics!!

hope i'm not too late!!

good luck

sorry one last quick note: you will need two types of triangles...this site shows a good example of the two types of triangles (dimensions) and the layout for a proper sphere...
http://www.dnaco.net/~michael/domes/kalenak/



[This message has been edited by Hoser_in_USA (edited 03-23-2000).]

Registered: Sep 1999
Location: Texan in Calgary for a while
Posts: 1361

Nhatman, cylinder is Pi*r^2*h right? I thought so, but didn't want to be wrong

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James Hromadka
VisorCentral.com
Personal Website: http://www.Hromadka.com

Registered: Mar 2000
Location: Hermosa Beach, CA
Posts: 222

Right-o-mundo, JHromadka!

As for the volume of the "sphere" that you'll be making, the smaller the triangles, the closer it will be to a real sphere, which means, you could get pretty close by using the volume of a sphere equation (4/3*Pi*r^3).

Good luck!

Registered: Nov 1999
Location: Kutztown, PA, USA
Posts: 106

well, we didn't win. We were going for the sphere, but it didn't work out good at all. So we went to a cylinder. that was going pretty good. But we still didn't have the max. Volume. One group who did a cube had the max. I think he measured our shape wrong. We knew we could make a Cube with 216, but we wanted to go higher then that. Yeah well, so much for trying something new.

Registered: Mar 2000
Location: Hermosa Beach, CA
Posts: 222

Sorry it didn't work out.

Too bad you couldn't do the sphere. You would've kicked their butts. With your 8x12 paper, you effectively would have 216 sq.in. of area, which could make a sphere of radius 4.146 in and volume of 298.5 in^3.

You would've blown away the cube-people with about 40% more volume!

Oh well....next time.