Question

A cube whose two adjacent faces are colored is cut into 64 identical small cubes. how many of these small cubes are not coloured at all?

Answer 1

The answer is 36 cubes...since two adjacent faces are coloured then 28/64 cubes will have atleast 1 side coloured

Answer 2

Given : A cube whose two adjacent faces are colored is cut into 64 identical small cubes.

To find : Number of small cubes which are not coloured at all

Solution:

Cube is cut into 64 identical small cubes

=> 4 * 4 * 4 = 64

=> Each face has 4 * 4 = 16 Cubes

Hence two adjacent face will

16 + 16 = 32 Coloured Cubes

but 4 cubes at the matching edge of both faces

will be common

hence total cubes ith coloured faces = 32 - 4 = 28

Small cubes not coloured at all =  64 - 28

= 36

36  small cubes are not coloured at all

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