Question

A cube is painted blue on three adjacent faces and cut into 216 smaller identical cubes.
(1) How many smaller cubes have only one surface painted ?
(2) How many smaller cubes have three face painted ?
(3) How many smaller cubes have at least one face painted ?​

Answer 1

The cube is painted on three adjacent faces and cut into 64 smaller, identical cubes. In this case, only one corner cube is painted on three of its faces.

Each pair, out of three coloured adjacent faces, has only one common edge. Thus, there are three edges, along which two coloured faces meet. There are three smaller cubes along each such edge which are painted only on two of their faces. Hence, there are totally 3×3=9 smaller cubes which are coloured on two of their faces. 

There are 9 smaller cubes on each coloured face which are coloured only on one of their faces. Thus, there are totally 9×3=27 smaller cubes which are coloured only on one of their faces.

Answer:

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Answer 2

Answer:

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