Question: Spherical particles whose radii have the density function fR(r) are dropped on a mesh as in Problem. Find an expression for the density function of the particles that pass through.

Problem: A sieve is made of a square mesh of wires. Each wire has diameter d, and the holes in the mesh are squares whose side length is w. A spherical particle of radius r is dropped on the mesh. What is the probability that it passes through? What is the probability that it fails to pass through if it is dropped n times? (Calculations such as these are relevant to the theory of sieving for analyzing the size distribution of particulate matter.)