Question

A carton can hold 1000 unit cubes that measure 1" x 1" x 1" what are the dimensions of the carton using unit cubes

Answer 1

The volume of the carton doesn't tell you the dimensions.

Without cutting up any of the little cubies, the 1000 of them could be
packed into a carton with any of these sets of dimensions:

1 x 1 x 1000
1 x 2 x 500
1 x 4 x 250
1 x 5 x 200
1 x 8 x 125
1 x 10 x 100
1 x 20 x 50
1 x 25 x 40

2 x 2 x 250
2 x 4 x 125
2 x 5 x 100
2 x 10 x 50
2 x 20 x 25

4 x 5 x 50
4 x 10 x 25
4 x 25 x 100

5 x 5 x 40
5 x 8 x 25
5 x 10 x 20

10 x 10 x 10