Question

the total volume of a cube is 360 inches to the third power how do you write 2 different possible sets of diminsions for the cube

Answer 1

If it's really a cube, then it can have only one set of dimensions.
Actually, only one dimension ... the length of every edge is the
same number.

The volume of a cube is the cube of its edge length.  So the
length of every edge is the cube root of its volume.

But the dimension can sometimes be written in different ways.

Volume = 360 inch³

Edge length =  ∛(360 inch³)

                    = ∛360  inches

                    =  3 ∛(13 and 1/3)  inches

                    =  4 ∛5.625  inches

                    =  5 ∛2.88    inches

                    =  6 ∛(1 and 2/3)  inches  .

Answer 2

Well,

Since it's a cube, there will only be one real dimension, and that will be the cube root of 360.

$\sqrt[3]{360} = 2\sqrt[3]{45}\ inches$

The only way to write different dimensions is to write using different units.

12 in. = 1 ft.

$\frac{2\sqrt[3]{45}}{12} = \frac{\sqrt[3]{45}}{6}\ feet$