 how much in a roll of 100 dollar bills? sonhouse Posers and Puzzles 14 Jun '11 06:24
1. 14 Jun '11 06:24
Saw a movie where the protagonist pulled out a roll of 100 dollar bills about 5 cm in diameter. I googled how thick is that bill, 100 of them stacked is 1 cm. So how much does a roll 5 cm in diameter represent? We can make the assumption the inner diameter was 1 cm, like a toilet roll.
2. 14 Jun '11 06:57
English man. What the heck is five centimeters in inches? American english.
3. 14 Jun '11 08:142 edits
Originally posted by 4nonprophet
English man. What the heck is five centimeters in inches? American english.
0.043 inches is the thickness of a 100 dollar bill. 5 cm X 2.54 =1.96 inches. If you add one more 100 dollar bill, the thickness is just over 2 inches. You really should know inch to metric conversion factors since we have to live with both systems. 2.54 cm = one inch. 25.4 mm also = one inch. One foot = 304.8 mm, or 30.48 mm.
4. 14 Jun '11 15:22
As far as I can tell with google, the present 100 dollar bill is 6.14 X 2.61 inches or 156 X 66 mm.
5. 14 Jun '11 17:591 edit
So it looks like the first layer of bills, bill in this case, wrapped around a 0.39 inch diameter roller would wrap around just under 5 times. So that first layer, the single hunkie, will be 0.215 inch thick. Doesn't bode well for our rich friend....

That is about 5 mm metric. 5.461 to be more exact. The next layer starts a bit short of the 5 deep, doesn't start for a bit becoming the next layer.
6. 14 Jun '11 22:471 edit
Originally posted by sonhouse
So it looks like the first layer of bills, bill in this case, wrapped around a 0.39 inch diameter roller would wrap around just under 5 times. So that first layer, the single hunkie, will be 0.215 inch thick. Doesn't bode well for our rich friend....

That is about 5 mm metric. 5.461 to be more exact. The next layer starts a bit short of the 5 deep, doesn't start for a bit becoming the next layer.
That method seems a bit laborious.

consider the area occupied by the roll of bills when standing. (A)

A = pi {(2.5)^2 - (0.5)^2}
(difference of two squares ... I knew that would come in handy one day!)
A = 6pi

The area a 100dollar bill standing edge on occupies is
a = .01 * 15.6
a = 0.156

So the number of 100dolar bills required is 6000pi/156 ... about 120

EDIT: all measurements in cm or sqcm
7. 15 Jun '11 05:062 edits
Originally posted by wolfgang59
That method seems a bit laborious.

consider the area occupied by the roll of bills when standing. (A)

A = pi {(2.5)^2 - (0.5)^2}
(difference of two squares ... I knew that would come in handy one day!)
A = 6pi

The area a 100dollar bill standing edge on occupies is
a = .01 * 15.6
a = 0.156

So the number of 100dolar bills required is 6000pi/156 ... about 120

EDIT: all measurements in cm or sqcm
Sounds about right, I was guestimating about 180. Where did the 6000 come from?
Oh, never mind, I saw it, 6PiX100. Not sure about the 100 though.

The standing on edge thing, where did you get 0.01? Is that supposed to be the thickness in what, mm? Google has it 0.043 inches thick times 25.4 gives 1.09 mm as thickness. 1.09 X 156 or around 170 mm squared.
8. 16 Jun '11 09:111 edit
Originally posted by sonhouse
Sounds about right, I was guestimating about 180. Where did the 6000 come from?
Oh, never mind, I saw it, 6PiX100. Not sure about the 100 though.

The standing on edge thing, where did you get 0.01? Is that supposed to be the thickness in what, mm? Google has it 0.043 inches thick times 25.4 gives 1.09 mm as thickness. 1.09 X 156 or around 170 mm squared.
6pi/0.156 = 6000pi/156

thickness taken from your earlier post:
"I googled how thick is that bill, 100 of them stacked is 1 cm"
9. 16 Jun '11 15:17
Originally posted by wolfgang59
6pi/0.156 = 6000pi/156

thickness taken from your earlier post:
"I googled how thick is that bill, 100 of them stacked is 1 cm"
That number might be off a few percent, they probably rounded it out. The number I read in inches is 0.043 which would be 0.43 inch which is a bit over 1 cm. If I ever get my hands on a 100 dollar bill I would measure it with my digital calipers to verify that. My present financial state indicates that will be a long time coming🙂
10. 17 Jun '11 02:58
Originally posted by sonhouse
That number might be off a few percent, they probably rounded it out. The number I read in inches is 0.043 which would be 0.43 inch which is a bit over 1 cm. If I ever get my hands on a 100 dollar bill I would measure it with my digital calipers to verify that. My present financial state indicates that will be a long time coming🙂
I find it hard to believe that US bills are 1mm thick!!
Surely that is wrong?
11. 17 Jun '11 14:187 edits
Originally posted by wolfgang59
I find it hard to believe that US bills are 1mm thick!!
Surely that is wrong?
I'll dig out my calipers, I can only test the smaller ones, unless I go to the bank, they might let me play with a C note for awhile. But it can't be a whole lot different than a 1 dollar bill I would think. News at 11.

1 mm is 0.039 and change of an inch. So if it really is 43 thou, it is a bit more than a mm. 1.0922 mm to be exact. Assuming it is 43 thou though.

Well SOMEONE fed us a pile of BS. A CD is 0.045 inch, about 1.1 mm thick. Obviously money is a lot thinner. I found my digital calipers and measured regular printer paper which comes out at 0.004 inch, one tenth of a mm.

We actually had a C note, it turns out to be thinner than a piece of printer paper:

0.003 inch, switched the calipers to mm and it comes out as 0.09 mm.

So 100 bills would be 90 odd cm. Since the accuracy of my calipers is only 2 digits at that thickness, the actual thickness would have to be verified if someone had a stack of 100 bills.... Any volunteers?🙂

Only off by a factor of about 10!

Using my own measurements of a 100 dollar bill, it is 2.59 inches wide and a bit over 6 inches long, I had to do a double measurement of that since my caliper is only good to 6 inches, it seems to be about 6.1 inches long. Doing it in mm, 2.59 inches=~65.8 mm, 6.1 inches=~155 mm long. So 65.8X155X0.1=1023.2 mm cubed. The roll at 50 mm wide minus the inner 10 mm=1884mm squaredX65.8mm=123967 mm cubed, dividing the two gives about 121 bills to fit that roll. So we are in agreement and this time with much better size figures. So the grand total comes out to 12100 bucks. Not a bad days work, eh.
12. 20 Jun '11 17:48
It's easier to consider this in terms of volume.
The volume of one \$100 bill is .0043*2.16*6.14 = 0.057028 square inches.

The volume of the cylinder minus the hole is 2.16*(.98425)^2*pi - 2.16*(.19685)^2*pi = 6.13082 square inches

divided by volume of one bill = 110.66 bills.
I'm guessing some space is taken up by the air and what not between the bills, so I'd guess that there are really about 105 bills. = approximately \$10500
13. 21 Jun '11 06:39
Originally posted by Savielly
It's easier to consider this in terms of volume.
The volume of one \$100 bill is .0043*2.16*6.14 = 0.057028 square inches.

The volume of the cylinder minus the hole is 2.16*(.98425)^2*pi - 2.16*(.19685)^2*pi = 6.13082 square inches

divided by volume of one bill = 110.66 bills.
I'm guessing some space is taken up by the air and what not between the bills, so I'd guess that there are really about 105 bills. = approximately \$10500
Not easier. You have just multiplied through by the width of the bill (which incidently you got wrong).
14. 21 Jun '11 19:31
Originally posted by wolfgang59
Not easier. You have just multiplied through by the width of the bill (which incidently you got wrong).
We both got the same answer, about. He may have just computed the roll as if rolled up vertically instead of horizontally. I think it would be about the same as far as diameter goes.
15. 22 Jun '11 15:12
I don't understand, the radius of this supposed "roll" Benjamins isn't constant...It would be in theory a "spiral". Who rolls money into perfect cylinders ( or as close to perfect as can be achieved with sheets of paper of constant length)? But i'm just being picky.