Verbal Reasoning - Cube and Cuboid - Discussion

The following questions are based on the information given below:

  1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
  2. The opposite faces of dimensions 4 x 3 are coloured yellow.
  3. The opposite faces of other dimensions 4 x 3 are coloured red.
  4. The opposite faces of dimensions 3 x 3 are coloured green.
  5. Now the cuboid is cut into small cubes of side 1 cm.

3. 

How many small cubes will have no face coloured ?

[A]. 1
[B]. 2
[C]. 4
[D]. 8

Answer: Option B

Explanation:

Number of small cubes have no face coloured = (4 - 2) x (3 - 2) = 2 x 1 = 2


Mano said: (Apr 28, 2011)  
How we can find it as (4 - 2) x (3 - 2) ?

Sakthi said: (Aug 25, 2011)  
To find the faces that have not been colored can be given by the

formula(x-2)^3,

for a cube l, b, h are same so can directy use, whereas for cuboid.

Since they ve different dimensions,

its given as (l-2) *(b-2)*(h-2)

here l=4 other values are 3,

So, 2*1*1 =2

Rakeshsoni said: (Oct 2, 2017)  
Can anyone explain this?

Pinky said: (Aug 10, 2018)  
Total cubes = 4*3*3 = 36.

Cubes with 3 faces coloured = 8.
Cubes with 2 faces coloured = 16 (6+6+2+2).
Cubes with 1 face colured = 10 (2+2+1+1+2+2).
So, cubes with no coloured face = 36-(8+16+10) = 36-34 = 2.

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