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Side of an empty cubicle carton = 9 cm.

Now as we know that volume of the cube is the cube of its side.

So the volume of an empty cubicle carton having side 9 cm, V = ${\left( 9 \right)^3} = 729{\text{ c}}{{\text{m}}^3}$.

Now we have to find out can 1000 cubes of side 1cm fit in it.

So the volume of the cube of side 1 cm is, V’ = ${\left( 1 \right)^3} = 1{\text{ c}}{{\text{m}}^3}$

So the volume of the 1000 such cubes = 1000 (1) = 1000 cubic centimeters.

Now if the ratio of the volume of the empty cubicle carton to the volume of 1000 cubes of 1 cm is greater than 1 then we can will 1000 cubes of side 1 cm into an empty cubicle carton otherwise not.

So the ratio of the volume of the empty cubicle carton to the volume of the 1000 cubes is,

$ \Rightarrow \dfrac{V}{{V'}} = \dfrac{{729}}{{1000}} = 0.729$ < 1