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.

1. 

How many small cubes will have only two faces coloured ?

[A]. 12
[B]. 24
[C]. 16
[D]. 12

Answer: Option C

Explanation:

Number of small cubes having only two faces coloured = 6 from the front + 6 from the back + 2 from the left + 2 from the right

= 16


Udayakumar said: (Jan 2, 2011)  
Can anyone please explain this?

Santosh said: (Feb 23, 2011)  
Please explain this problem.

Narendra Kirar said: (Jun 11, 2011)  
Please suggest any simple and shortcut answer.

Sakthi said: (Aug 25, 2011)  
Could not understand how its two from left and right, hope its 3.

Mrudula said: (Sep 8, 2011)  
Can some one explain this?

Shekhar Ghate said: (Nov 6, 2011)  
The formula for cubes having two sides painted is
(L-2)x4 + (B-2)x4 + (H-2)x4 Where L = Length, B= Breadth, H=Height
In the above problem it is (4-2)x4 + (3-2)x4 + (3-2)x4
i.e 8 + 4 + 4 = 16

Prasanna said: (Nov 16, 2011)  
Thank you shekar.

Raghavan said: (Feb 3, 2012)  
Hi, refer the picture again. Note the Between the right side top cornor. The cube having 2 colored faces. Simultaneously bottom side cube having 2 colored faces. Thats why 2 came.

Raghavan said: (Feb 3, 2012)  
Could you tell me how does L-2*4 comes?

Deep said: (Dec 18, 2012)  
From front, how is it 6 cubes. ?

From front only 4 cubes are two face coloured.

Vishal said: (Apr 10, 2013)  
2 cubes of green yellow face and 4 cubes of yellow red face.

Drashti said: (Jun 23, 2013)  
Is the formula given by @Shekhar applicable for any cuboid to find cubes with two side painted?

Nimesh said: (Jul 29, 2013)  
Its the right explanation. If you go through it practically you would surely get it right.

Vindy said: (Jun 11, 2014)  
What is the reason of multiply by 4?

Aadharsha said: (Jan 5, 2015)  
I think so 4 from left and 4 from right. 4 cubes have two face colored.

Vignesh said: (Mar 5, 2015)  
I too had problems on left and right side cubes. @Aadharsdha, do you find it?

Vinothini said: (Sep 2, 2016)  
In my point of the view, 12 is the answer.

Aditya said: (Oct 20, 2018)  
Since there are 12 edged in the cube front face have 2 faces such as 2 sides painted so total 2*4 (edges of 2 sides painted), similarly when you go by height 1*4, and same breadth 1*4.

So, total (2*4 + 1*4 + 1*4) = 16.

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