CAT - Question of the Week

Question: A cube of side 12 cm is painted black on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted? 

Ans: A 12 cm side when cut into equal sections of 3 cm each, will comprise 4 such sections.

Hence, total number of smaller cubes = 4 x 4 x 4 = 64

All the smaller cubes that form the outer walls of this solid mass, will have atleast one of their faces painted black.

The only cubes with none of their faces painted lie at the center.

Excluding one cube for each of the sides from the earlier equation, the number of cubes at the center are :

(4-2) x (4-2) x (4-2) = 2 x 2 x 2 = 8

Hence there are 8 such cubes.

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