Question

The internal dimensions of box are 1.2m ,80cm and 50 centimetre.how many cubes each of edge 7cm can be packed in the box with faces parallel to the sides
of the box. Also,find the space left empty in the box

Answer 1

Find the multiples of 7 closer to 120, 80, 50 which are 119, 77, 49.
Calculate their product which is 1309(7³) cm³.
Hence, 1309 cubes of edge 7cm can be put in the box.
Left-over volume is (120-119)×(80-77)×(50-49) = 3 cm³.

Answer 2

Internal dimensions are  l=120cm ,b= 80 cm and h=50
  Hence the volume of box = 480000cm²
When cubes are position would occupy 17*7=119 cm in length with 1cm gap
                                       similarly         11*7= 77 cm in width   with 3 cm gap
                                       and                 7*7 = 49cm in height  with 1 cm gap
Hence no of cube can be packed =17*11*7=1309
volume occupied = 119*77*49=448987
Space left empty= 480000 - 448987=31013 cm³