Coffee Can with Dimes
TM
: G. Exoo (g...@fred.indstate.edu) wrote:
: : I have a 16 ounce coffee can filled with dimes. I wonder how much
: : money is in it? The can is exactly full to the top, has been repeatedly
: : shaken to the point where shaking the can causes no more settling. I'm
: : curious how close an estimate one can make without weighing the can. All
: : the dimes in the can are of the new cheap U.S. variety.
: cheap dimes???? What are they worth now, about ten cents??
: Yes I know what you're saying. Just being an intelligent-butt.
: I estimate $10
Duh, call me stupid. It's weigh more than $10. More like a hundred or
maybe 2 or three hundred. I'll say one-fitty.
: : Geoff Exoo
: : Indiana State University
: : g...@fred.indstate.edu
: "TM"
David Savitt
>I have a 16 ounce coffee can filled with dimes. I wonder how much
>money is in it? The can is exactly full to the top, has been repeatedly
>shaken to the point where shaking the can causes no more settling. I'm
>curious how close an estimate one can make without weighing the can. All
>the dimes in the can are of the new cheap U.S. variety.
A 1990 U.S. dime weighs 2.268 grams, and is composed of 8.33% nickel and the
rest copper. It is not indicated whether the 8.33% is by weight, or by volume.
Nickel's density is 8.902 grams/cm^3 and copper's density is 8.960 grams/cm^3.
By volume: let V be the volume of the dime. Then
(V*8.33*8.902+V*91.67*8.960)/100=2.268 g => V=.253 cm^3
By weight: V=2.268/100*(8.33/8.902+91.67/8.960) => V=.253 cm^3
There is very little difference in the volume estimate, in fact not down to the
5th decimal place. This estimate is reasonable because, combining this with the
fact that the diameter of a dime is 1.791 cm, this gives the thickness of a
dime as precisely .100 cm.
First method (precise): Fill the coffee can with water (with the dimes inside).
Pour off the excess water into a measuring cup. Take the difference between
that volume and the volume of water that fills the can when empty (or just
assume that that's exactly 16 oz), convert to cm^3, and divide by .253 cm^3
per dime. Actually, you might run into trouble with water clinging to dimes,
to the container, etc., so you may want to fill the empty can completely with
water, and then add the dimes back to the can while carefully collecting the
water spilling over. Alternately, take a big measuring cup, put in enough
water to submerge the dimes, and add the dimes in, noting the rise in the
water level. For really disgusting precision, you'll want the water at 25
degrees Celsius (77 F) as that's the temperature at which the density figures
were taken, and you'll want to let the dimes adjust to that temp.
Second method (throwing precision out the window): Assume that the dimes fill
the whole coffee tin. Now, 16 oz=28.88 in^3=473.2 cm^3, so
# Dimes ~ 473.2/.253 ~ 1870 dimes.
Perhaps the dimes take up some very high percentage of but not the whole tin.
If the dimes occupy 80% of the space, perhaps a low estimate, that's 1500 dimes.So there's probably about $170+/-10 in the tin.
-Dave
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Dave Savitt | 2nd year mathematics | AKA Little Dave | Go Canucks!
dsa...@unixg.ubc.ca | University of B.C. | AKA Goliath | Go Capitals!
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G. Exoo
I have a 16 ounce coffee can filled with dimes. I wonder how much
money is in it? The can is exactly full to the top, has been repeatedly
shaken to the point where shaking the can causes no more settling. I'm
curious how close an estimate one can make without weighing the can. All
the dimes in the can are of the new cheap U.S. variety.
TM
: I have a 16 ounce coffee can filled with dimes. I wonder how much
: money is in it? The can is exactly full to the top, has been repeatedly
: shaken to the point where shaking the can causes no more settling. I'm
: curious how close an estimate one can make without weighing the can. All
: the dimes in the can are of the new cheap U.S. variety.
cheap dimes???? What are they worth now, about ten cents??
Yes I know what you're saying. Just being an intelligent-butt.
I estimate $10
: Geoff Exoo
: Indiana State University
: g...@fred.indstate.edu
"TM"
Tom Magliery
>
>: I have a 16 ounce coffee can filled with dimes. I wonder how much
>: money is in it? The can is exactly full to the top, has been repeatedly
>: shaken to the point where shaking the can causes no more settling. I'm
>: curious how close an estimate one can make without weighing the can. All
>: the dimes in the can are of the new cheap U.S. variety.
I've got a 12oz coffee can here that looks to be about 6 inches tall.
A stack of 10 dimes looks to be about 3/4 of an inch tall, so I'd
guess around 80 layers of dimes would fit in the can. I'd guess about
20-25 dimes or so would fit in a layer, so I'll guess 25x80=2000 dimes,
or about $200. But wait, you said a 16oz can, so I'll just bump that
up by 1/3(ish) and say $265.
Be sure to let us know what the actual answer is sometime. :-)
mag
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Jonathan Haas
Does the person who comes closest get the money? ;-)
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David Savitt
>Second method (throwing precision out the window): Assume that the dimes fill
>the whole coffee tin. Now, 16 oz=28.88 in^3=473.2 cm^3, so
># Dimes ~ 473.2/.253 ~ 1870 dimes.
>Perhaps the dimes take up some very high percentage of but not the whole tin.
>If the dimes occupy 80% of the space, perhaps a low estimate, that's 1500 dimes.So there's probably about $170+/-10 in the tin.
It's been pointed out to me by Tom Magliery that a 16 oz coffee tin is by
weight and not 16 fluid ounces. He's right, of course, and I've just measured
the volume of such a tin at 45 1/2 ounces. That gives 187*45.5/16=530 dollars
of dimes. That seems too high. I think that there may be more useless space in
such a tin filled with dimes than I previously thought. If 80% of the space
is filled, however, that gives $425 in the tin.
Scotholemeau
friend Carrie was making cake, and she measured the Crisco by dunking it
in water and measuring it volumetrically (sp). \
So I guess that you could do the same thing with the dimes in the coffee
can. And it wouldn't matter how densely they were packed. Fill the full
cann with water, dump out the water, measure it's volume, then the
volume of the can, and finally the volume of a single dime. This should
give a very good estimate of the amount of beer money in the can,
depending on how good you are with a ruler.
Scott