Step 1: Geometry:
Look at one face of the cube. Three atoms lie in a line along the diagonal: corner, face centre and opposite corner, so the diagonal holds 4 radii.
Step 2: Work:
Diagonal $= 408\sqrt{2} = 577$ pm. Divide by 4: $r = 144.2$ pm.
Step 3: Check:
Using the wrong relation $r = a/4$ would give 102 pm, and the bcc relation gives 176.6 pm. Neither is an option except by confusion. Option (C) is right.
Final Answer:
Option (C), 144.2 pm.
\[ \boxed{\text{(C) } 144.2\ \text{pm}} \]