How far away is safe?

Geometry Level 4

Imagine a planet made up of an atmosphere of one layer of paint balls, each of 1 meter diameter. This planet is 1000 meters in diameter. This planet is about to explode and all neighboring spacecrafts have been advised by the Alliance to move to a distance where the chance of them being hit by a paintball is equal or less than 1%. Imagine your spacecraft is a sphere of 10 meters diameter, how far away is the minimum distance (to the nearest 500 meters) from the surface of the exploding planet you would have to fly to be considered safe?


Assume the diameter of the planet to be the distance from the central axis of one paint ball to the central axis of another paint ball on the other side of the planet.

Assume the paint balls to be tightly and magically packed such that there are no interstitial spaces at all

Assume all the magical paint balls explode outwards perpendicular to the surface of the planet


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