I failed higher math in high school...miserably...but would like some help trying to figure this one out. Don't know if this is the right place on the forum but here we go. If a more appropriate spot on the forums please move there!

Say I have a particle that's 15 microns in diameter and let's assume it's perfectly spherical. Then you break that particle (volume) up into particles that are 1 micron that are also perfectly spherical. What is the approximate increase in surface area going from 1 15 micron particle/sphere to multiple (amount ?) 1 micron particle/spheres that will fit into the original volume of 1 15 micron sphere? Seems like you will lose some volume with a bunch of 1 micron spheres stuffed inside a 15 micron sphere but think you get the picture. I'm looking for close but exact, supported by an explanation, would be PRIMO! If perfectly round 1 micron spheres how much volume is lost in the space between these spheres if stuffed into that original 15 micron sphere? This info would be some gravy.

To recap I'm interested in knowing what the increase in surface area is going from 1 15 micron sphere to multiple (amount ?) 1 micron spheres that fit within that 15 micron space. My head hurts just thinking about it.

Thx for any help!