Acarton can hold 1000 unit cubes that measure 1 inch by 1 inch by 1 inch .describe the dimensions of the carton using unit cubes

All we can tell about the carton is ...

-- Its length is a number 'L' inches.
-- Its width is a number 'W' inches.
-- Its height is a number 'H' inches.

-- 'L',  'W',  and  'H'  are whole numbers.

-- The product of  (L · W · H)  =  1,000 .

We can't tell anything else about what the numbers L, W, and H are.

They could be  10,  10,  and  10 .
They could be  1,  1,  and  1,000 .
They could be  1,  2,  and  500 .
They could be  1,  10,  and  100 .
They could be  2,  4,  and  125 .

There are many other sets of numbers that they could be.
We just have no way to know.