The staggering number of water drops is roughly 6.0⋅1023.
First, we need to find out the distance between Earth and the moon at perigee, which is the closest point to Earth the moon reaches in its orbit. This distance is listed at 225,804 miles, which, after converting to km, equals 363,396km.
We can now determine the volume for our water column. Starting from its rectangular base of 9.2 X 9.2km, we get
Vwater=9.2⋅9.2⋅363,396=30,757,837km3
Each km3 has 1⋅1015cm3, so the volume can be said to be
Vwater=30,757,837⋅1015cm3.
Now, there are approximately 20 drops in 1cm3 of water, so the number of drops in a column this size should be
numberdrops=20drops1cm3⋅30,757,837⋅1015cm3→
numberdrops=615,156,740⋅1015, or roughly 6.0⋅1023
I've just noticed how close to Avogadro's number, which is 6.022⋅1023 molecules per 1 mole of substance...very good problem for trying to visualize and understand the concept of mole.
