Question

Khamba has some cubical boxes and each box has a different volume. The
smallest box has a volume of 1 cubic cm, and the biggest box has a volume of
8000 cubic cm. The length of sides of all the cubes is a natural number. What
is the maximum number of boxes Khamba can have?​

Answer 1

Step-by-step explanation:

vol of a cube = a³

so the smallest cube= 1cm³

a³=1cm³

a= ³√1cm³ =1cm

and vol of the biggest= 8000cm³

a³= 8000cm³

a= ³√8000cm³=20cm

Therefore, the number of cubes with the length of sides between 20 and 1 = 18 different cubes excluding the smallest and biggest.

overall the maximum number of cubes = 20.