How do you determine the dimensions of a rectangular prism that is 10 cubic feet?

Answer 1

you can't. If all you have is the volume, it could be

a cube of side ∛10
or, a brick with sides
1 x 2 x 5
2 x 2 x 2.5
4 x 2 x 1.25
10 x 5 x 0.2
etc.