#### Answer

See the answer below.

#### Work Step by Step

a) fcc, atoms are present in the all faces
b) tetrahedral holes, all of the atoms in "holes" are surrounded by four atoms each.
c) $8\times1/8=1$ in the vertexes, $6\times1/2=3$ in the center, 4 wholly within, 8 in total.
d) Mass: $8\times 28.085\ g/mol\div 6.022\times 10^{23}\ atoms/mol=3.731\times10^{-22}\ g/cell$
Volume: $(543.1\times 10^{-10}\ cm)^3=1.602\times10^{-22}\ cm^3/cell$
Density: $3.731\times10^{-22}\ g/cell\div 1.602\times10^{-22}\ cm^3/cell=2.329\ g/cm^3$
e) Projecting the point of a Si in a tetrahedral hole into the line connecting two Si, one in the corner and one in the face, we get a right triangle whose Face-Hole-Corner angle is half of the internal angle of a tetrahedron and the opposite side is half of the face diagonal:
$sin(109.5^{\circ}/2)=l/2.\sqrt2/2.r$
$r=235.13\ pm$