Hi Diana.
According to this source, a Canadian nickel is 21.2 mm in diameter and 1.76 mm thick.
The conversion factor you are looking for is 304.8 mm per foot. If you convert your floor's square footage to mm^{2}, you will get ( 400 ft^{2} ) x ( 304.8 mm / 1 ft)^{2} = 37 161 216 mm^{2}.
Now how many nickels will fit on the floor? Because nickels aren't square, their shape will play a factor in this. Here is a link that describes efficient ways of packing circles on a flat surface. The end result is that you can use the "hexagonal packing" method to cover 1/6(pi)sqrt(3) of the floor area with nickels.
So if we multiply the floor area by this figure, we get 33 701 495 mm^{2} of nickelcovered floor. How many nickels is that?
The surface area of side of a nickel is just the area of the circle whose diameter is 21.2 mm. Using the formula (pi)r^{2}, the area one nickel covers is 352.99 mm^{2}. If we divide this into the 33odd million, we get 95 475 nickels covering the floor.
Now we have to raise them to the ceiling. Using our conversion factor 304.8 mm/ft, the height of the room is 3048 mm. That divides into the thickness of the coin (1.76 mm) 1731 times, so we can multiply the nickels on the floor by 1731 to get the total number of nickels.
95 475 x 1 731 = 164 312 475 nickels.
Now that's a lot of change!
Stephen La Rocque.
PS: A nickel weighs 2.35 g, so the nickels in this room weigh over 386 metric tons. That's just about the maximum takeoff weight for a Boeing 747!
