So in other words, say you have a cube 15 cm at each direction, and you want 1 cm of armor for it all around. So you must subtract twice the armor thickness from each dimension, which would be a cube of 13 cm to a side.

Next, take the volume of the smaller from the larger, and the remainder is the armor volume. So in our example, 15cubed - 13cubed = 1178 cc out of 3375. About 1/3 of the total!

The method I suggested would be, 15squared x 6 = 1350. But remember, I did warn about when the armor got to be about 1/8 (maybe shoulda said 1/10th) of the total thickness, and here you see that the difference is significant. The reason my method is simpler, though, is because the book TELLS you the surface area, but unless your ship has a regularized shape, you cannot otherwise compute the exact surface area from the given dimensions. So you might be able to break your design down into its component shapes and figure it all out, but really, who wants to do all that work for no real gain?