Need Geometry help.

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DarkLogicianOfCaos

Eschew Obfuscation
I'm helping with an office prank and need some insight. I need to fill a room 10' x 11' x 7.5' (825 cu. ft.) with Balloons and need to know about how many I need to buy. Let's assume that the balloons will blow up to about 8" x 10" round. If they were square, it would be easy (8x10=80"/12=6.666' then 825/6.666'= 123.75 Balloons). See the porblem is, the balloons are oval and the space is square, so I need some space will be lost and some gained depending on how the balloons rest. Rough estimates are welcome, but showing the math will be even more helpfull as the exact size of the balloons won't be known until after we buy them. A mathimatical formula is best. Thank you. (It's for a surprise birthday/going away party).
 
Whatever estimate you get is going to be extremely rough, being that even if you got nothing but 10" balloons, there's still going to be a lot of variation between the balloons sizes, as the overall size is merely an estimate of what the person blowing up the balloon considers a "full" balloon.

You also need to consider the fact that latex balloons only stay inflated for roughly 6 to 8 hours. 10 if your lucky, and it needs to be a dry, cool place. So you'd need to have them inflated on the same day. The shear mass of balloons you'd need for a room that size (presuming your trying to flood the room, and even then) would require several store size helium tanks going at once (and not the store bought ones either, we're talking the 5 foot size tanks.)

I'm not trying to poo poo on your idea, mind you. But I feel you should get a sense of scale for what you describe. It would be rather massive, and no small task. And bear in mind, that it it will be very costly, unless you've got a good resource for balloons and helium. On the average a single 12" latex balloon will cost you $1.99 barring discounts for bulk quantities. Your looking at close to, if not over, 1000 balloons.

I'm sorry I don't have more mathematical figures to send ya, this is just what I'm already pretty sure of. Oh, and if you haven't figured it out by now, I used to be a supervisor at a major party supply chain. :D
 
Well, we are trying to fill the room. We have regular air tanks x2 (Helium is too expensive) and regular rubber-type balloons. Even so, 1000? Wow! OK, we will do our best. As for time/loss ratio, we will be setting this up at room temperature the morning of, approximately 2 hours before she gets there, so there, and since we are using regular air, we don't expect to loose too much air in that time. If we can only get the balloons up to 6sq.", I'm thinking 500 should get pretty close to the top? There are also a file cabinet, desk, table/chairs to take up some space, so..... Here's hoping. Maybe we can fill up the rest of the space with boxes wrapped like birthday presents....

Thanks for the help. I'll let you know how it goes!
 
This sounds suspiciously like homework. Or extra credit.

Anyway, you wouldn't need to fill the whole space with balloons, and I doubt it's possible to do so.
 
I think I recall the most closely packed way of packing spheres has half the unit cell being taken up by the spheres. That is, for every balloon there is an equal volume of air that cannot be taken up by another balloon.

Approximate a balloon to a 9" sphere. Volume of a sphere of diameter 9" is 4/3 pi r^3, is roughly 3054" square. Then (825*12*12*12/2)/3054 = 233 balloons.

EDIT: There, I fixed it. Forgot the "cubed" :p
 
DarkLogicianOfCaos said:
Well, we are trying to fill the room. We have regular air tanks x2 (Helium is too expensive) and regular rubber-type balloons. Even so, 1000? Wow! OK, we will do our best. As for time/loss ratio, we will be setting this up at room temperature the morning of, approximately 2 hours before she gets there, so there, and since we are using regular air, we don't expect to loose too much air in that time. If we can only get the balloons up to 6sq.", I'm thinking 500 should get pretty close to the top? There are also a file cabinet, desk, table/chairs to take up some space, so..... Here's hoping. Maybe we can fill up the rest of the space with boxes wrapped like birthday presents....

Thanks for the help. I'll let you know how it goes!
Click to expand...
So many years filling balloons with helium made me forget about that air tank we kept to the side. Yeah, air filled, if I remember correctly, will last a bit longer. I'd recommend you get started a bit earlier, though. Even with just a 100 balloon order we'd always get started early that morning to make certain we'd be on time for pick up. 500 could take a while.
 
How are you going to fill the last couple feet near the top of the ceiling? Opening the door, tossing in a balloon and slamming it really quickly probably won't work, although it could make for entertaining video. :D Does the office have a dropped ceiling? Maybe climb up in the adjoining office, remove a few panels and chuck them over the common wall....

edit:
Approximate a balloon to a 9" sphere. Volume of a sphere of diameter 9" is 4/3 pi r^3, is roughly 39" square. Then (825*12*12*12/2)/39 = 18,276 balloons.

Sounds pretty large to me. Maybe I did something wrong...
Click to expand...
LOL! For DLoC's sake I hope the math is off...
 
I'm pretty sure that's off. My wife and I we're thinking about it (she's the accountant), and let's say you've got 12" ballons filled full. I might be being a little conservative at saying you can get 4 into that much space. 4 x 825 = 3300. Yikes
 
Ok, I'm going with the 250 count and getting 500. Photos will be difficult as the doors open inward. I will do my best though. Thank you all for your input. Here goes nothing, tomorrow.
 
I come up with about 427 or so: 825 divided by 4/3 x pi x .67 x .83 x .83 (volume of the room divided by the volume of 1 ballon with estimated values for 10" x 18" round ballon); maybe round the volume of the ballon to 2 and you get around 412 or so. Because the room is in feet I used the dimensions of the ballon in feet also. If this totally wrong someone please let me know.


Don't forget to subtract the volume of the room already filled and the variations of each ballon size and the fact that the room is a rectangle and the balloons are ellipsoids (Man I can't believe I still remember this math stuff because I"m a lawyer, but then again it can be wrong); kind of remember my old calculus teacher stating that we had to use integration to get the answers to problems like these, are you sure this isn't a math problem and there are no real balloons involved, anyway it's enough for me to go to bed....
 
Well the thing turned out to be a bit of a flop. Rather disappointing really. the guy who started this whole thing went budget crisis on us and only got about 200 balloons. I wish he would have told me he was only going to get that few, I would have picked up the rest. Moreover, while he did get some 20" and most were 9", he went for variety, so he ended up with a couple of packs of long narrow and small round, which, while it looked different, did not do anything to fill the office up. We basically got it about knee deep by the time we were done. In practical terms, DJ's rough estimate of 1,000 turned out to be closer to what we would have needed. Time-wise, 3 hours was more than enough time, but near the end, by cohort's fingers started bleading from tying the ballons off, so he definatly wouldn't have last through 1,000. I was fine, but then again, I finger tighten/loosen screws a lot so I have calluses.

As for pictures...How do I get them on here? Copy/Paste doesn't seem to work.
 
Go to http://img110.imageshack.us/ and upload the pictures from your computer. It's free and painless.

Then take the "Direct link to image" link at the bottom of the page and paste in bewteen these two tags:

HTML: 
[img][/img]


For example this:
HTML: 
[img]http://img360.imageshack.us/img360/6388/edmontonamusementparkrosh2.jpg[/img]
will look like this:

edmontonamusementparkrosh2.jpg
 
okay, let's see if I did this right. Again, it is no where near what I was hoping for...

setup1dp8.th.jpg


completesc1.th.jpg


openiy6.th.jpg


poppedil4.th.jpg


We got them about desk high, still making impossible to get into her office (faces have been blurred for privacy). We blew them up in the warehouse where it was about 50 degrees, and for some reason her office was about 70+, so as the day progressed, the balloons would *pop* by themselves. Each time one did you would hear one of the girls sceam. It was great. After a few hours though their boss decided they weren't getting enough work done with all the screaming and popping, so he came in and popped them all.
 
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