A box whose shape is a parallelepiped can be completely filled with cubes of side
![1.](/media/m/f/6/7/f67f08c0471cbb9c2f13e29a08d9579d.png)
If we put in it the maximum possible number of cubes, each ofvolume,
![2](/media/m/e/e/e/eeef773d19a3b3f7bdf4c64f501e0291.png)
, with the sides parallel to those of the box, then exactly
![40](/media/m/1/d/3/1d365c6c26bfc819b1701bd64fa621ba.png)
percent from the volume of the box is occupied. Determine the possible dimensions of the box.
%V0
A box whose shape is a parallelepiped can be completely filled with cubes of side $1.$ If we put in it the maximum possible number of cubes, each ofvolume, $2$, with the sides parallel to those of the box, then exactly $40$ percent from the volume of the box is occupied. Determine the possible dimensions of the box.