Answer:
No 1 inch cubes will fit
28 one-half inch cubes will fit
Explanation:
No cubes with a side length of 1 inch will fit because one dimension of the prism is only 1/2 inches, so we can't fit a 1 inch cube in anywhere.
Since one dimension is 1/2 inch, we can line up 1/2 inch cubes along the other 2 dimensions. Let's say that the 1/2 inch dimension is the base, the 2 inch dimension is the height, and the 7/2 inch dimension is the length.
We can stack the cubes 4 high, (2 inches of height with 1/2 inch being the cube height, there are 4 halves in 2).
We can place 7 cubes along the length (7/2 inches = 3.5 inches. There are 7 halves in 3.5).
So we can have 4(7) = 28 one half inch cubes can fit in to the prism