Verified Answer :

IwAsSoMeGuY

18 unit cubes means that the area of the rectangular prisms (cuboids), will be 18 cm^3
We need to work out the three factors that can be multiplied to get 18. Let's start simple and give the cuboid a height of one. That means we need to work out heights and lengths that are factors of 18. Factors of 18 are:

118
29
36

So there we have three cuboids, of dimensions 1118, 129, and 136
Now things get more complicated. We need to use the other factors of 18 as heights. Let's start with a height of 2. This means that the height and length of the rectangle need to be factors of 9, because 18/2 = 9.
Factors of 9 are:

19
33

So that gives us two cuboids, of dimensions 219 and 233
Use the next factor, which is 3. 18/3 = 6, so the height and length have to be factors of 6. Factors of 6 are:

16
23

So that gives us two cuboids, of dimensions 316 and 323
At this point, we don't need to go through any more factors, because they will all certainly end up with the same dimensions as the previous ones we've found

Our final cuboids are 1118, 129, 136, 219, 233, 316, 323
Now we need to eliminate all the duplicates. 
129 = 219
136 = 316
233 = 323
So we'll just get rid of all the ones on the right hand side, because they're equivalents of the ones on the left
So we end up with cuboids of dimensions 1118, 129, 136, 23*3

Hope that helps, I know some of that may be confusing, you can comment/pm and I'll try to explain it more :)

The correct answer is:

He can make four different rectangular prisms using these cubes.

Explanation:

We use the factors of 18 to answer this question. We want three factors of 18 at a time. To find these factors, we use our divisibility rules.

Every number is divisible by 1. 18/1 = 18; we can have a rectangular prism with dimensions 1 x 1 x 18.

Since 18 is even, it is divisible by 2: 18/2 = 9. 9 = 3 x 3; this gives us 2 x 3 x 3 for the prism.

Using 2 again, we also have 2 x 9 x 1.

The digits of 18 are 1 and 8; the sum of these is 9. Since this is divisible by 3, then 18 is divisible by 3; 18/3 = 6. This gives us 3 x 6 x 1 for the prism.

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