Final answer:
The total surface area of a tower of n cubes, each with side length s, accounting for only the exposed surfaces, is 2s²n + 2s². None of the provided options exactly match this expression, but option B is the closest.
Step-by-step explanation:
To determine the total surface area of a tower made up of n cubes, each with a side length s, without counting the faces that cover each other, we can use the surface area formula for a single cube. For one cube, the surface area is 6s². However, since cubes are stacked on top of each other, only the top and bottom faces of the entire tower and the four side faces of each cube are exposed.
There are n cubes, so the exposed side area is four times the area of one face of a cube, multiplied by the number of cubes, which is 4ns². Adding the two single faces on the top and bottom, which do not get covered, the total surface area becomes 4ns² + 2s² = 2s²(2n + 1). However, since the problem statement doesn't account for faces that cover each other, we omit the bottom face of each cube except for the very first cube in the tower. This modification leads to the simpler formula: 4ns² + 2s² (for the bottom cube), finally simplifying to 2ns² + 2s².
If we simplify this expression by factoring out 2s², we get 2s²(n + 1), which is not one of the provided options. Thus, a mistake seems to have occurred either in the options or in interpreting the question. The formula for a tower should consider the surface area of all the side faces plus two more squares for the top and bottom faces. Assuming the question indeed requires this total, the expression close to this concept is 2ns², matching option B, but the correct total should be 2s²(n+1) or 2s²n + 2s².