Question

eight wooden spheres with radii 3 in. are packed snugly into a square box 12 in. on one side. the remaining space is filled with packing beads. what is the volume occupied by the packing beads? what percentage of the volume of the box is filled with beads?

Answer 1

vbox-vspheres

vbox=, I assume we are dealing with l=w=h
so
v=lwh=12^3=1728

vsphere=(4/3)pir^3
r=3
vsphere=(4/3)pi3^3=4pi9=36pi
8 of them so
8 times 36pi=288pi or about 904.7786842338604526772412943845 cubic inches



vbox-sphere=1728-904.7786842338604526772412943845=823.2213157661395473227587056155
space filled by packing beads is about 823.22 cubic inches
beads percent is 823.2213157661395473227587056155/1728 times 100=47.64% filled by beads