Question

A large cube is painted on all six faces and then cut into a certain number of smaller but identical cubes. It was found that among the smaller cubes, there were eight cubes which had no face painted at all.
How many smaller cubes was the original large cube cut into?

Answer 1

Answer:

As there are 6 such faces, the number of such smaller cubes will be 16*6 = 96. Lastly, the number of cubes having no faces painted can be found by subtracting the sum of the painted cubes from the total number of smaller cubes. Therefore, the required answer is 216 – (8 + 48 + 96) = 64 cubes.

Answer 2

The original cube was cut into 64 identical smaller cubes.

• It is given that there are eight cubes with all the surfaces not coloured.

• They are cut out from the inner part of that bigger cube. Assembling that into a smaller cube, we will have a foundation on which all the painted cubes can be placed to get the complete cube.

• These eight small cubes can form a larger cube with a side length equal to two smaller cubes. This way, we will have 2*2*2 = 8 cubes.

• Now, if we imagine, the painted cubes are to be added to form a bigger cube. We will have to increase cube length on each of the four sides of the surface. Doing this, the side length will increase to 4.

Therefore, the total number of cubes cut = 4*4*4 = 64 cubes.