Explanation:

Let’s break it down:

- Suppose the original cube has side \( a \).

- Its volume is \( a^{3} \). Cut it in half, so each cuboid has volume \( \frac{a^{3}}{2} \).

- The simplest way: cut along a plane parallel to a face. Each cuboid is then \( a \times a \times \frac{a}{2} \).

- Surface area of the original cube: \( 6a^{2} \).

- Surface area of one cuboid: Two faces are \( a \times a \), four are \( a \times \frac{a}{2} \). So,

\( 2(a^2) + 4(a \cdot \frac{a}{2}) = 2a^2 + 2a^2 = 4a^2 \).

- So the ratio \( \frac{6a^2}{4a^2} = \frac{3}{2} \) or 3 : 2.

Let’s look at the options:

- Option 1: 2 : 1 —— Not matching.

- Option 2: 3 : 2 —— This matches our answer.

- Option 3: 4 : 3 —— Doesn't match.

- Option 4: 5 : 3 —— Nope.