Cuboid Surface Area: Analyzing a Three-Dimensional Rectangular Prism

To find the surface area of a cuboid, we consider its six rectangular faces. A cuboid has three pairs of opposite faces. Each pair of faces shares the same area.

The surface area $S$ of a cuboid with dimensions $a$, $b$, and $c$ is calculated by finding the area of each of these rectangular faces and then summing them up. Specifically, we consider:

• The area of the first pair of opposite faces with dimensions $a$ and $b$ is $ab$.
• The area of the second pair of faces with dimensions $b$ and $c$ is $bc$.
• The area of the third pair of faces with dimensions $a$ and $c$ is $ac$.

The total surface area is thus given by the formula:

$S = 2(ab + bc + ac)$

By analyzing the provided choices, it's clear that the correct formula for the surface area of the cuboid is $2(a\times b + b\times c + a\times c)$.

Therefore, the solution to the problem is $2(a \times b + b \times c + a \times c)$.