Final answer:
Using 8 unit cubes, one can build three different rectangular prisms, considering the possible integer dimension combinations that make up the number 8.
Step-by-step explanation:
To determine how many different rectangular prisms one can build using 8 unit cubes, we need to consider the possible ways to arrange these cubes so that they form a prism. A unit cube has dimensions of 1x1x1, so we are looking for all the integer factor combinations of 8 that will result in a rectangular prism. The factors of 8 are 1, 2, 4, and 8. These factors give us the following distinct rectangular prisms:
It's important to note that the prism 2x4x1 and 4x2x1 are not included separately as they are the same as 1x2x4 when rotated. Therefore, we have a total of three different rectangular prisms that can be formed with 8 unit cubes.