Why do we need to measure the volume?

We need to measure volume to check capacity of substance, to see that how much material it can hold inside it.

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

source:  

i believe it is the square root of 122 because when you turn it on it's side, to where the 5 inches is on the bottom, it looks like it is the same length.