A cubical box without a top is 4 cm on each edge. it contains 64 identical 1cm cubes that exactly fill the box. How many of these small cubes actually touch the box?

52

Step-by-step explanation:

A cubical box without a top is 4 cm on each edge containing 64 identical 1 cm cubes.

We have to find the number of small cubes that actually touch the box.

Now, there are 4 layers of 16 cubes from bottom to top.

In the bottom-most layer, all the 16 small cubes will touch the bottom of the large cube.

Again, from the top three layers, only the outer small cubes will touch the sides of the large cube.

So, there are 12 small cubes in each top three layers that will touch the large cube.

Hence, in total there will be (16 + 12 * 3) = 52 small cubes that actually touch the large cube box. (Answer)