Stacking the stepladders.

If we want to fill the $10 \times 10 \times 10$ area, we need to have no empty spaces in between. The formation needs to be as compact as possible. If we take two stepladders, and try to fit them as compact as possible in a $2 \times 2 \times 3$ area, we will end up with two empty spaces, which will be in the opposite corners of one of the $2 \times 3$ sides.

Now, if we look at one stepladder piece and imagine it inside a $2 \times 2$ cube, every side of the cube will have at least two $1 \times 1$ cubes in it. Thus, you can't put a stepladder piece exactly under the $2 \times 2 \times 3$ area that will fit in one of the empty spaces. The only way you can fit it in is if protrudes out of the area, but that will leave a gap that cannot be filled by a stepladder.

Thus, you cannot fit stepladders into a $10 \times 10 \times 10$ area.