A syntactic foam is made by mixing thin-walled hollow glass spheres (radius, r, and wall thickness, t=0.05r) into an epoxy resin, which is then cured and hardened. The glass from which the spheres are made is twice as dense as the hardened resin.
If the spheres are identical and randomly packed with a volume fraction of 0.45, what is the density of the syntactic foam, in terms of the resin density, ρr? Note that the volume of a sphere is Vs=43πr3 and that, for a thin-walled sphere, the volume of the spherical shell is Vshell=4πr2t .
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