Latest CTS Aptitude Question SOLUTION: Questions 21-25: A cube painted red on two adjecent faces and black on the faces opposite to the red faces and green on the remaining faces is cut into sixty-four smaller cubes of

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Questions 21-25: A cube painted red on two adjecent faces and black on the faces opposite to the red faces and green on the remaining faces is cut into sixty-four smaller cubes of equal size. 21. How many cubes are there which have no face painted ?

Asked In CTS Roshni (9 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

Ram  (9 years ago)

Since all faces are painted, only small cubes which are in the middle of cube will have no color painted.
Total smaller cubes=64
Small cubes which are atleast 1 side is coloured
= top(16 cubes)+ bottom(16 cubes)+ both sides(16 cubes)+ both sides adjacent to previous sides(8 cubes)=16+16+16+8=56
so cubes with no paint=64-56=8
answer is 8 cubes

Is this solution Helpfull? Yes (11) | No   

sribardhan  (9 years ago)

o Face Painted-------> (n-2)^3 * 1
1 Face Painted-------> (n-2)^2 * 6
2 Face Painted-------> (n-2)^1 * 12
3 Face Painted-------> (n-2)^0 * 8 ALWAYS 8

Is this solution Helpfull? Yes (10) | No (1)  

ishani  (9 years ago)

3 colored faces-8 corners=8
2 colored faces-2 per edge=2*12
1 colored face-4 per face-4*6
left-64-24-24-8=8 !

Is this solution Helpfull? Yes (3) | No (1)  

SUDHIR SHARMA  (9 years ago)

use this formula , (x-2)^3 ,where x is the side of the bigger cube.
i.e (4-2)^3 = 8
Therefore, 8 cubes will not have no face painted.

Is this solution Helpfull? Yes (2) | No (1)  

Chirag Ranjan Lahiri  (9 years ago)

(n-2)^3
here total number of small cube=64
hence n=4
then,(4-2)^3=8

Is this solution Helpfull? Yes (2) | No (1)  

arun rathore  (9 years ago)

As given the large cube is cut 64 equal size cubes it means 64 is the net volume of the large cube hence.
Let x is side of larger cube
X(3)=64
X=4
Now side of cube with no painted surface
4-2=2
Now volume of this cube
2(3)=8
Hence this cube can be cut into 8 equal size cubes hence 8
Ihope everyone understood

Is this solution Helpfull? Yes (2) | No   

Annu Kumari  (9 years ago)

(n-2)^3
here total number of small cube=64
hence n=4
then,(4-2)^3=8

Is this solution Helpfull? Yes (1) | No   

ani roy  (9 years ago)

sudhir sharma how did u get 4 in the formula?

Is this solution Helpfull? Yes | No (2)  

Nemichandra Hombannavar  (9 years ago)

10
9*6= 54. total cubes having some color on them. So 64-54=10

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Sandeep Kumar  (9 years ago)

cut will be like 3*3*3. so in mid of the cube only 1 cube will be there whose no face painted .

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praneethreddy soma  (9 years ago)

all the cubes are having atleast one face painted except the middle one.so the answer is 1

Is this solution Helpfull? Yes | No (3)  

bastab kr layek  (9 years ago)

use this formula , (x-2)^2 ,where x is the side of the bigger cube.
i.e (4-2)^2 = 4
Therefore, 4 cubes will not have no face painted.

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sukhchain  (9 years ago)

27 cubes are there which have no face painted

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Jyothsna  (9 years ago)

16
4*4*4=64
if 6 faces are painted with 3 colors and when we cut the cube into 64 cubes then cubes which are inside are not get painted and the cout of those cubes will be 16

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