How many nickels will fit in a 2 liter bottle

A nickel has a diameter of 21.21 mm and a thickness of 1.95 mm 

2.121 cm diameter 
0.195 cm thickness 

Think of a nickel as a cylinder 

r = 2.121/2 = 1.0605 cm 

V = pi * r^2 * h 
V = pi * 1.0605^2 * 0.195 cubic cm 

2 liters = 2000 cubic cm 

2000 / (1.0605^2 * 0.195 * pi) => 
2902.84713216 

Your upper limit is 2902, but it could be as little as 0 (for instance if the 2L bottle was only 1 cm wide, then you wouldn't be able to fit a single nickel in there) 

I'd say that you could expect about a 70% packing efficiency, just off the top of my head 

2900 * 0.7 => 
290 * 7 => 
300 * 7 - 10 * 7 => 
2100 - 70 => 
2030 

I'd expect around 2000 nickels would fill up the bottle quite nicely, supposing you can get the nickels into it.