How long will it take to cover the moon with spherical miniature meteors, one meter tall, each with a diameter of #1.00xx10^-6# meters, hitting the moon at a rate of 1 meteor per second?
It will take
My first attempt to answer this was wrong, because the question was wrong. Apologies if I caused any confusion. The questioner meant to say the meteors are covering 1 square meter of the moon per second (not one meteor per second). This allows us to answer the question using just surface area.
The moon has a surface area of
That's one million meteors stacked on top of each other, to make a pillar of meteors one meter tall. So the at the rate of one square meter per second, the first layer of meteors would take
That is, one second for each square meter of the surface. Now you have to calculate this times one million (the number of meteors in a 1 meter tall pillar). So the answer is
Converting to years, this is almost