"I am a figure with six layers .each of my layers is the same."---> using this sentences, you can conclude that the shape is cube because cube made of 6 similar square.
my bottom layer has a perimeter of 28 units ---> Using this sentences, you can know the square perimeter is 28. Then the square side would be:
square perimeter= 4* side
28= 4* sides
side= 7
Then, the volume of the cube would be:
cube volume= side^3
cube volume= 7^3= 343 cubic units
I think there is a typo somewhere in this question. The calculation should be true, but it is not in 200-300 range. The volume that in 200-300 would be when the side is 6 unit(volume=216), but the perimeter should be 24 not 28.
If the perimeter 28, volume= 343
If the perimeter 24, volume= 216