Aptitude Overflow
+1 vote
26 views

A cube of side $12$ cm is painted red 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?

  1. $16$
  2. $8$ 
  3. $12$
  4. $24$
asked in Quantitative Aptitude by (4.1k points)  
recategorized by | 26 views

1 Answer

0 votes

The big cube is cut into 4 x 4 x 4 = 64 small cubes 

There are 8 original corners - 3 painted sides 
There were twelve edges on the original cube - each will give two cubes with two painted sides - 24 in all 
There were 6 faces - each with four cubes with one painted side - 24 in all 

So the number with no painted sides is 64 - 8 - 24 -24 = 8 
(The unpainted cubes formed a small cube 2 x 2 x 2).

OR

no of cubes N = 12 / 3 = 4
formula: no of cubes having 0 faces painted = ( N - 2 ) ^ 3 = ( 4 - 2 ) ^ 3 = 2 ^ 3 = 8

similarly formula for 2 face painted = 12*(N-2)
for 1 face painted = 6 * ( N - 2 ) ^ 2

Option B is the Correct Answer.

answered by (1.5k points)  

Related questions

2,599 questions
936 answers
376 comments
31,320 users