$(1)$ Assume a spherical pore as shown in the schematic above. Calculate the size of

the pore $($which would have a radius $r)$ that would exist between these four powder

particles that have particle sizes of $150m.$

$(2)$ Determine what is the maximum size for a spherical guest particle to be filled in

the center pore of the cube. What is the radius ratio of this guest particle vs$.$ the

initial sphere?