To estimate the time it would take to completely fill the cubic box on the moon with micrometeorites, we need to calculate the volume of the box and compare it to the number of micrometeorites landing inside it each second.
The volume of the cubic box is given by the formula V = l³, where l is the length of one side of the cube. In this case, the length of one side of the box is 1.5 meters, so the volume of the box is V = (1.5 m)³ = 3.375 m³.
Now let's look at the number of micrometeorites landing inside the box each second. We know that one micrometeorite lands per square meter of the moon's surface each second. Since the box has an area of (1.5 m)² = 2.25 m² on each side, the number of micrometeorites landing inside the box each second is 2.25.
To find out how long it would take to fill the box completely, we need to divide the volume of the box by the number of micrometeorites landing inside it each second:
Time = Volume / Landing rate
Time = 3.375 m³ / 2.25 micrometeorites/s
Simplifying the equation:
Time = 1.5 seconds/micrometeorite
Therefore, if one micrometeorite lands in the box each second, it would take approximately 1.5 seconds to completely fill the box with micrometeorites.