1. It takes 8 unit cubes to fill a 2x2x2 prism because if you stack 8 unit cubes together, you get a block that is 2 units long, 2 units wide, and 2 units high. This is the same size as the 2x2x2 prism. Each face of the 2x2x2 prism is made up of four unit squares, and each unit square can be filled by a single unit cube. Therefore, to fill the whole 2x2x2 prism, you need a total of 8 unit cubes.
2. To fill a 2x2x2 prism with cubes that are 1/2x1/2x1/2, we need to first figure out how many of those smaller cubes would fit into a single unit cube. Since each side of the small cube is half as long as each side of the unit cube, the volume of the smaller cube is 1/8th that of the unit cube. Therefore, it would take 8 of the smaller cubes to fill a single unit cube.
Next, we need to figure out how many unit cubes would fit into the 2x2x2 prism. Since the prism is 2 units long, 2 units wide, and 2 units high, it has a volume of 8 cubic units. Since each unit cube has a volume of 1 cubic unit, it would take 8 unit cubes to fill the prism.
Finally, since it takes 8 of the smaller cubes to fill a single unit cube, we can find the total number of small cubes needed by multiplying the number of unit cubes by 8:
8 (unit cubes) x 8 (small cubes per unit) = 64
Therefore, it would take 64 of the 1/2x1/2x1/2 cubes to fill a 2x2x2 prism.