Answer: 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 = (9)3=729 cm3.
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’ = (1)3=1 cm3
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,
⇒VV′=7291000=0.729 < 1
So as we see that the ratio is less than one so we cannot fit 1000 cubes of side 1 cm into an empty cubicle carton of side 9 cm.
Explanation:
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