Question

it take 64 cubes to fill a cubical box that has no top. how many cubes are not touching a side or the bottom of the box?​

Answer 1

Answer:

Each small cube would have dimensions $1\times 1\times 1$ making each cube a unit cube.

If there are $16$ cubes per face and there are $5$ faces we are counting, we have $16\times 5= 80$ cubes.

Some cubes are on account of overlap between different faces.

We could reduce this number by subtracting the overlap areas, which could mean subtracting 4 cubes from each side and 12 from the bottom.

$80-(4\times 4+12)=80-28=52=\boxed{B}$

Solution 2