Question

The outer surface of a 4 cm x 4 cm x 4 cm cube is painted completely in red. It is sliced parallel to the faces to yield sixty four 1 cm x 1cm x 1cm small cubes. How many small cubes do not have painted faces?

a) 8
b) 16
c) 24
d) 36

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Answer 1

the number of small cubes which do not have painted faces are 8.
because 8 smaller cubes which is the inner most part of the larger cube and does not have any coloured part and does not have any connection with the coloured part of the outer cubes.

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Answer 2

Option A. i.e. 8

Only 8 cubes will left without any paint on any face.

number of cubes on outer surface in center = 6x4 = 24
number of cubes on outer surface at edge center= 12x2=24
number of cubes on outer surface on corners = 8

remaining cubes = 64-24-24-8=8

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