Question

An empty carton is of side 9cm. can you fit in 1000, 1 cm cubes in it,?​

Answer 1

Step-by-step explanation:

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,

cubicle carton to the volume of the 1000 cubes is,⇒V/V′=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.