A3. A cube with edge length $a$ is cut into 8 smaller congruent cubes. The surface area of one such small cube is denoted by $P$. What is $P$?
(A) $\frac{a^{2}}{2}$
(B) $\frac{3 a^{2}}{4}$
(C) $\frac{a^{2}}{8}$
(D) $\frac{3 a^{2}}{2}$
(E) $a^{8}$
A3. Let $a_{1}$ denote the length of the edge of the smaller cube. Considering that the volume of the smaller cube is $a_{1}^{3}=\frac{a^{3}}{8}$, we get $a_{1}=\frac{a}{2}$. Therefore, it follows that $P=6 a_{1}^{2}=6\left(\frac{a}{2}\right)^{2}=\frac{3 a^{2}}{2}$.