Question

Rosa has 16 unit cubes. How many different rectangular prisms can she build with the cubes?

Answer 1

`4`

Explanation:

Since the rectangular prism is formed by the unit cubes, each dimension of the prism must be a whole number of cubes.

Given that Rosa has `16` unit cubes, so we need to find the total number of different combinations of three whole number that have a product of `16`.

To find these combinations, look at the factors of `16`.
They are `1,2,4,8 and 16`.

Pick any two of these factors and determine if there is a third value from this list so that the product of the three factors is `16`

There are `4` combinations that will work :
`1xx1xx16`
`1xx2xx8`
`1xx4xx4`
`2xx2xx4`

Hence, Rosa can build 4 different rectangular prisms with 16 unit cubes.