Latest TCS Aptitude Question SOLUTION: Samita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of cubes needed to make a hollow cube looking of the same shape? If we are painting only 2 fac

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Samita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of cubes needed to make a hollow cube looking of the same shape? If we are painting only 2 face of each cube then how many faces will remain unpaint???

Solution

If we consider the question same as printed then answer by @SI-IW@NI 12U13EY is correct but
if we change the second statement as follows-
If we are painting only 2 of the face of the cube with dimensions 5*5*5 then how many faces of the cubes with dimensions 1*1*1 will remain unpainted
then answer by PAYEL is correct


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Asked In TCS Arvind Pareek (12 years ago)

Solved Read Solution (8)

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Read Solution (8) :

Payel  (12 years ago)

Vol of the outside cube = 5*5*5=125
Vol of the hollow part inside the outside cube = 3*3*3=27
No.of cubes required to make a hollow cube of same shape= 125-27=98

Total no of faces= 98*6=588
No of faces painted=5*5*2=50
No of faces that remain unpainted=588-50=538

Is this solution Helpfull? Yes (26) | No (6)  

@SI-IW@NI 12U13EY  (12 years ago)

For a full 5*5*5 cube, we will use 5*5*5 = 125 cubes of size 1*1*1
However, we are leaving the internal of the cube hollow.
The internal of the cube is actually a cube of size 3*3*3
To make such a cube, we need 3*3*3 = 27 cubes of size 1*1*1
Thus, the number of cubes we need to make such a hollow cube will be:
125 - 27 = 98 cubes of size 1*1*1


For your second question, I assume you are talking about the faces of the 5*5*5 cube.
Each cube, regardless of size, has 6 faces.
Thus, the 5*5*5 cube will have 6 - 2 = 4 unpainted sides.

If you are talking about the 1*1*1 cubes, since there are 98 of them, we will have:
98*4 = 392 unpainted faces.

Is this solution Helpfull? Yes (25) | No (14)  

surbhi  (12 years ago)

can u plzz tell y is iit (5-2)??

Is this solution Helpfull? Yes (11) | No (1)  

Harsh Gupta  (12 years ago)

no of hollow cube === 5*5*5 - (5-2)*(5-2)*(5-2)
=== 98
no of face unpainted === 392

Is this solution Helpfull? Yes (5) | No (4)  

P.K.DHARMA  (12 years ago)

538 is the answer

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

Arvind Pareek  (12 years ago)

can u explain answer.....

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

Prasenjit Boral  (12 years ago)

for the second part of this question we have total 98 small cubes. total faces=98*6 =588 4 faces of large cube is unpaintad. area of each face for large cube = 25 area of each face of smaall cubes =1 , so in each face of large cube there are 25 face of small cubes. painted faces of small cubes = 25*2=50 unpaint faces 588-50=538

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

ssour  (12 years ago)

98 is the answer

Is this solution Helpfull? Yes | No (4)  

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