Question

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

Answer 1

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.