Latest Accenture Aptitude Question SOLUTION: 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 painte

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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?

Asked In Accenture X22 (13 years ago)

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bharath krishna  (13 years ago)

If a cubic block of n*n*n individual cubes is taken, and the outer layer of cubes is removed (which is essentially what you are doing in this question), you will be left with a block of (n-2)*(n-2)*(n-2) cubes.

There will always be 8 cubes with 3 faces painted (the corner cubes)

A cube has 12 edges
Each edge will have (n-2) cubes that are not corner cubes
There will be 12(n-2) cubes that have 2 faces painted.

A cube has 6 faces
Each face will have (n-2)^2 cubes that have only one face painted.
There will be 6(n-2)^2 cubes that have only one face painted

Unpainted cubes: (n-2)^3
One face painted: 6(n-2)^2
2 faces painted: 12(n-2)
3 faces painted: 8

(n-2)^3 + 6(n-2)^2 + 12(n-2) + 8
= n^3 - 6n^2 + 12n - 8 + 6n^2 - 24n + 24 + 12n - 24 + 8
= n^3 cubes in total

In this question n=4
Unpainted cubes: 2^3 = 8
One face painted: 6*2^2 = 24
2 faces painted: 12*2 = 24
3 faces painted: 8

Is this solution Helpfull? Yes (22) | No (6)  

ETWARI KUMAR  (9 years ago)

there is a formula : n = 12/3 , (n-2)^3, now (4-2)^3= 8 ans

Is this solution Helpfull? Yes (3) | No   

parul maheshwari  (9 years ago)

8 .cube is divides into 64small cubes....n since all faces are painted then only the inner middle cubes are not painted.....slice it into 3 cuts.....4Horizontal parts are separated....nw 2nd slice contions inner 4 small cubes wwhich are not painted n also 3rd slice 4 inner middle cubes are nt painted ..therefore ans is 4+4=8

Is this solution Helpfull? Yes (1) | No   

Ranjeet kumar  (9 years ago)

(12/3)^3=64

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ravi ranjan  (9 years ago)

64 cube is having 12cm side ,so when it is cut into 3cm different cube
there are 64 cubes

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tamilmani  (9 years ago)

4
the inside 4 cubes are not painted

Is this solution Helpfull? Yes | No (1)  

tamilmani  (9 years ago)

8
The center 8 cubes

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Mayank Kumar  (9 years ago)

8 small cubes

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Harish  (7 years ago)

8
Coz only outer once will be painted not the correct ones....

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