Question

An empty cubicle carton is of side 9 cm. Can you fit in 1000 cubes of side 1 cm in it?

Answer 1

Hint: In this particular question use the concept that the volume of the cube is the cube of its side, so if the ratio of the volume of the empty cubicle carton to the volume of 1000 cubes of 1 cm is greater than 1 than we can will 1000 cubes of side 1 cm into an empty cubicle carton otherwise not, so use these concepts to reach the solution of the question.

Complete step-by-step 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 = ${\left( 9 \right)^3} = 729{\text{ c}}{{\text{m}}^3}$.
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
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.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall the volume formula of the cube which is stated above, so first find the volume of the empty cubicle carton then find the volume of the 1000 cubes then divide them as above if the resultant is less than 1 then we cannot fit 1000 cubes in to an empty cubicle carton and if greater than 1 we can fit 1000 cubes in to an empty cubicle carton having side length 9cm.