how many pepsi cans fit into cargo space of 36 cu ft?

Curius-- How about you meet a Researcher partway for that big $2
payment and go measure a Pepsi can?

The answer could depend to some extent on the shape of the 36 cubic
feet.  If it is very long and wide but only one inch high, the answer
would be zero.

Also, are there restrictions on stacking?  Can some cans be upright
and others sideways?  Do they need to be kept in the purchasing
packages of twelve or more, or can they be individually put in the
cargo bay?

Well, we can at leat get an approximate upper bound fairly quickly.
Now the canonical soft-drink can is 375mL, so with an allowance for
the can itself I'll call each can 400mL. 36 cu ft is 28.3 L (assuming
I've calculated that correctly), so it looks like at most 70 cans or
so - using 375mL per can gives us 75 cans max.

As other posters have mentioned, a lot depends on the precise shape of
the cargo space; for maximal efficiency it could be shaped like a
really, really tall cylinder just wide enough to fit a can (or 70-odd
cans) inside, and as previously mentioned it might be impossible to
get any cans inside. But whatever shape, you won't get any more than
70-75 cans in it.

Manuka,

You have indeed defined the most efficient shape for the 36 cubic feet
of space with your really, really tall cylinder.  But I think that a
liter is less than a cubic foot.  I pulled a standard 12 fluid ounce
soft drink can out of the fridge (and drank it).  The label says it
has 354 milliliters in it.  I looked up the conversion factor from
cubic inches to liters.  It is 61.02374 cubic inches per liter.  This
amounts to 21.60240538 cubic inches per can.  There are 1728 cubic
inches per cubic foot.  Therefore there are 79.99 cans per cubic foot
or 2879 cans per 36 cubic feet.  Of course even with your maximally
efficient shaped space, the cans have a ridge on top and something
similar on bottom.  So less cans would fit.  The above calculation in
essence, assumes that we have one big can.

Before we pursue it any further, I think Curius should measure his can
of Pepsi for us.  I must say though, this problem is much more
interesting if it is academic rather than practical.

Here is a link to Erich's Packing Center

http://www.stetson.edu/~efriedma/cirinsqu/

It shows the most efficient packing arrangements for circles in
squares.  Depending how this problem plays out, this could be relevant
in some way.

I got as far as the Pepsi website and found that the cans are only 8
oz, at least no others were mentioned.

A lot. More than 12,000 cans.

That is based only on about 1/4 inch as the thickness of the flattened
pepsi can. So if the cans are to be run over by a real heavy roller
compactor, the type they use in road construction, I bet more than
15,000 cans will fit inside your 36-cu.ft. cargo space.

Are you in the business of recycling alum cans?

Model a coke can as a perfect cylinder with a volume of 12 fl oz =
0.012533 cu. ft.  Assume that the cargo space is a rectangular prism
that fits tightly around rectantularly stacked cans.  Then each can
takes up a block of space with a square cross section, and the volume
it takes up is greater than the volume of the can by a factor of 4/pi
(the ratio of the area of a square to the circle that fits inside it).
 So the volume taken up by each can is 0.015957 cu. ft., and 2256 of
them will fit in your cargo space.

Of course, you could fit a few more if you where to stagger rows of
cans so that they fit together like a honeycomb, but I'm assuming the
cans stay in their plastic 6-pack holder ring-things.  If you do
'stagger' the cans, and you have not gotten extremely creative with
the shape of your cargo space, there is an upper limit of 2605 cans. 
This is assuming the cross-sectional area taken up by each can is
greater than the actual cross section of the can by a factor of
2*sqrt(3)/pi, which is tightest you can pack circles into a plane.

According to some website, a soda can is 6" high with a 2" diameter. 
That's ~24"^3.  A cubic foot is 1728 cubic inches.  That's 72 cans per
cubic foot.  To make sure it makes sense conceptually, that would be
two 6x6 stacks.  Sounds about right.  So 72x36 is 2592.  Initally the
> 2000 figures posted by others did not make any conceptual sense to
me, so a coworker and I made a back of the envelope check.  And after
some thinking, the conceptualization is a bit more clear, though 2500
still sounds somewhat high to me.

Let's see:  36 cubic ft is 1.02 cubic meters or 1020 liters.  That
divided by 375 ml (or 0.375 ltr) is 2,718.4, the max. number of
contents of cans of that size that would go in a TANK of 36 cubic ft. 
BUT, we are stacking cans so we lose some space.  Base area of a can: 
3.14159r^2; area of the square it occupies:  4r^2.
Thus stacked cans occupy only 0.7854 of the base area each requires (3.14159/4).
This reduces the volume of Pepsi in 36 cubic ft to 2,135 cans, and we
must subtract something for the space lost from the shape of the ends
of the cans and the bit of air space within them.
This is getting pretty close to the 2000 can estimates.
Personally, I prefer Ticbol's answer.

"BUT, we are stacking cans so we lose some space.  Base area of a can: 
3.14159r^2; area of the square it occupies:  4r^2."

Iff you stack in squares, yes, but you can also stack in triangles and
hexagons, a bit like honeycomb...

S

There are a few different ways to pack cans into a rectangular space. 
I?m just using the three most common (and most efficient) methods
below:

Assuming Aligned Cans:
__________
|()()()()|     
|()()()()|                            /
|()()()()|                          H/    __
                                    /__  (__)
                                   |  W // / <soda can
Assuming staggered Cans:          D|   (/_/  
___________      __________        | 
|()()()() |      |()()()()| 
| ()()()()|  or  | ()()() |
|()()()() |      |()()()()|

w=width, d=depth, h=height (bear in mind that the cans that will fit
depend on which side is determined to be ?up?.  Laying the cans down
in the box will have the same effect as rotating the box). 
Measurements are in inches, as this is based on a 2?x2?x6? can.

In the first case the optimal number of cans would be
floor(w/2)*floor(d/2)*floor(h/6).

If mod(w,2)>1, the staggered arrangement will have the same number of
cans in each row.  The maximum number of cans in this case would be
floor(w/2)*floor(((1.1547*d)-.3094)/2)*floor(h-6)

In the event that mod(w/2)<1 you?d be better of using the aligned can arrangement.

If you copy the following formulas into Excel (with ?WIDTH:? on cell
A1) this should calculate the number of cans that can fit into the
specified box.  Just replace the ???s with the dimensions (in inches).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

WIDTH:
?
DEPTH:
?
HEIGHT:
?

STAGGERED:
=FLOOR(A2/2,1)*FLOOR(((1.1547*A4)-0.3094)/2,1)*FLOOR(A6/6,1)

ALIGNED:
=FLOOR(A2/2,1)*FLOOR(A4/2,1)*FLOOR(A6/6,1)

MAX:
=MAX(A12,A9)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Sample Solutions:
24?x36?x72?  = 2952 cans (using the 72? side as the depth)
36?x36?x48?  = 2916 cans (using the 48? side as the depth)
40?x40?x40?  = 2640 cans (a cubic box is not optimal)
2?x2?x15552? = 2592 cans (a tower is also not optimal)
102?x101?x6? = 2958 cans (I believe this is the most possible)

OK, clearly the biggest problem here is inaccuracy in describing the
dimensions of a pepsi can.  I don't know if this changes from country
to country, but in the US, pepsi cans contain 12 fluid oz of pepsi,
which is 355 mL.  It says so right on the can.  There may be a bit of
air space inside the can, and the aluminum itself takes up some room. 
Also the cans aren't perfect cylinders, but taper in at the ends, and
the bottom is indented.  So I measured a can of Coke (I would have
used a Pepsi can, if the stuff wasn't so vile--I think the dimensions
are probably the same.)  2 inches in diameter by 6 inches high is a
very inaccurate description.  The diameter of my specimen was not very
constant (the can is not very round) but the average diameter, within
a fraction of a millimeter, is 66 mm, or 2.60 inches.  The overall
height of the can is 123 mm, or 4.84 inches.  However, the effective
height is a bit less, say 120 mm (4.72 in) because cans will 'nest'
together a bit, with the bottom rim of one fitting inside the top rim
of another.  Using these dimensions, the volume of the cylinder taken
up by a can is 13.9 oz or 411 ml or 25.1 cubic inches.  So if you
stack them 'six pack' style into a rectilinear 36 cubic foot space,
you can fit at most 1947 of them.  If you stagger them, the upper
limit is 2249.

Yes, indeed, Rracecarr, that two inch can was misleading,  This site
suggests that the most usual diameter for drinks cans is 65 mm,
probably the size of your can.
Of course I agree entirely with your +/- 2000 can solution.  :)  while
being a little pleased that my calculation based on the can volume,
regardless of the dimensions, gives this result.  Anse1001 should like
that too.

http://www.geocities.com/and_pollett/beer52.htm

Cheers, Myoarin

No, my can has a diameter of 66.0 mm.

the pepsi can dimensions are 
H=12 cms  / 4.5 in
W=6.5 cms / 2.2 in
330 ml in a can

This is country-specific - here in Australia the standard soft-drink
can has a 375 mL capacity, which is why I used that figure in my
calculation (pity I forgot to multiply the volume by 36 when I was
converting to litres). So it looks like our cans are a little bit
bigger than yours.

curius, even with the 12cm x 6.5cm can dimension, there are a few more
pieces of info one needs before getting an answer.

1. The number of cans that can fit in a 36 cu ft vary dramatically as
the dimensions of the space change.  What are the exact dimensions in
the space you'd like to pack with cans?

2. Can this be considered an abstract calculation or a physical one? 
By this I mean, could the 'cans' be substituted with 12x6.5 cylinders
or should I take the interlocking tops, the flexing of the aluminum,
or any other properties of the cans into account?

3. Just for my own curiosity...why do you want to know how many cans fit?

-Fractl