Question

exactly 512 small cubes perfectly fill a lidless cubical box. All of the small cubes were removed except those touching the bottom of the box and those touching the sides of the box. How many of the small cubes were removed

Answer 1

Answer: 216

Step-by-step explanation:

Since, a cube is a 3D structure,

We can understand this problem by assuming the figure in the coordinate axis.

In which, The cubes in the box along x-axis = 10

Along y-axis = 10

Along z-axis = 10

Total cubes along each x, y, z directions those are not appearing on surface are (10-2), (10-2), (10-2) = 8, 8, 8  

Therefore total cubes which are not shown on the surface of the cube= $6\times 6\times 6 = 216.$

Since, the box that are not in the surface are removed.

Thus, the total boxes that are removed = 216