$35 \cdot 61000$ unit cubes are combined to form a large cube with an edge length of 10 units, which is then painted and subsequently separated back into the original unit cubes. The number of unit cubes that have at least one face painted is
(A) 600 .
(B) 520 .
(C) 488 .
(D) 480 .
(E) 400 .
(24th American High School Mathematics Examination, 1973)
[Solution] There are $8 \cdot 8 \cdot 8=512$ internal unit cubes within the larger cube that are completely unpainted.
Therefore, there are $10^{3}-8^{3}=1000-512=488$ cubes that have at least one face painted. Hence, the answer is $(C)$.