Question

Two opposite surfaces of a cube are painted red

and all other remaining surface are painted

green, now it is cut in such a way that 125 small

and equal cubes are formed. Based on this

information answer the questions given below.

98. How many cubes will have their two surface

painted one red and other green?

a. 24

b. 27

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Answer 1

The answer is option B
When the painted cube is cute into 125 small equal cubes, we have:
A 3 faces painted cube on every corner
⇒Number of cubes with 3 face painted=1×8=8
Three 2-faces painted cube on every edge
⇒Number of cubes with 2 face painted=3×12=36
Nine single face painted cube on side
⇒Number of cubes with 1 face painted=9×6=54
∴ Number of cubes with no face painted=125−8−36−54=27