Question

How many 100 dollar bills will fit in a cubic foot?

Answer 1

First of all, we need to compute the volume of a 100 dollars bills. A quick search on Google tells us that

"The $100 bill is the same size as all other US currency. All US paper currency is 2.61 inches wide and 6.14 inches long, 0.0043 inches thick and weigh 1 gram"

So, since the bill is a rectangular prism, its volume is given by the product of its three dimensions. So, you have

$V = 2.61 \times 6.14\times 0.0043 = 0.06890922$ cubed inches.

Now, the volume of the bill is expressed in cubic inches, while the volume of the container is expressed in cubic foot. We need a conversion, and since there are 12 inches in 1 foot, there are $12^3 = 1728$ cubic inches in a cubic foot.

So, we have a volume of 1728 cubic inches, and we want to know how many 0.06890922-cubed-inched bills we can fit in it.

Since one bill has a volume of 0.06890922 cubic inches, $k$ bills have a volume of $0.06890922k$. We want to choose $k$ in such a way that it fill a 1728 cubic inches volume, so the equation is

$0.06890922k = 1728 \iff k = \dfrac{1728}{0.06890922} \approx 25076.47$

So, about 25 thousands bills would fit in a cubic foot.