Answer
See the answer below.
Work Step by Step
a) Carbon $8\times1/8=1$ in the vertexes, $6\times1/2=3$ in the faces, 4 in total.
Silicon: 4 in tetrahedral holes.
SiC
b) Similarly as in problem 47: The right triangle formed by a half of the tringle: corner C, hole Si and face C, has the C-Si-midpoint angle of 109.5$^{\circ}$/2 and the side opposite to that angle is a quarter of the face diagonal.
$sin(109.5^{\circ}/2)=l.\sqrt2/4\div Si-C$
$l=436.1\ pm$
Mass: $4\times(28.085+12.011)\ g/mol\div6.022\times10^{23}=2.663\times10^{-22}\ g$
Volume: $l^3=8.294\times10^{-23}\ cm^3$
Density: $m/V=3.212\ g/cm^3$
