Latest TCS Aptitude Question SOLUTION: a hollow cube of size 5 cm is taken,thickness=1 cm. it is made into smaller cubes of size 1 cm, if 1 face of the outer surface of the cube is painted, how many faces of the smaller

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a hollow cube of size 5 cm is taken,thickness=1 cm. it is made into smaller cubes of size 1 cm, if 1 face of the outer surface of the cube is painted, how many faces of the smaller cubes remain unpainted?

Asked In TCS Souradeep Guhathakurta (8 years ago)

Unsolved Read Solution (16)

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MONIKA SARAN  (8 years ago)

total no of smaller cubes= 25+25+15+15+9+9=98
painted face of bigger cube=1=25 small faces
total faces of smaller cube=98*6=588
remaining unpainted faces=588-25=563

Is this solution Helpfull? Yes (6) | No   

Shashank Sourabh Singh  (8 years ago)

vol of big cube= 5^3-3^3=98
so no of small cube =98
so no of faces in smallcube =98*6=588
1 face of big cube is painted means 25 faces painted in small cube
so unpainted face in small cube is =588-25= 563

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Shantanu Gautam  (8 years ago)

total no of smaller cubes= 25+25+15+15+9+9=98
no. of phases of bigger cube painted=1 = 25 small cubes
therefore total no of unpainted cubes=98-25=73

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Sudeshna Paul  (8 years ago)

Number of smaller cubes=25*2+15*2+9*2=98
Number of faces of smaller cubes=98
Number of faces of smaller cubes painted=25
Number of unpainted faces=98-25=73

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Deepak kumar kumawat  (8 years ago)

volume of bigger cube 5*5*5= 125
so there is 125 smaller cubes
1 face is painted of bigger cube
so unpainted smaller cubes 125-25=100

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Rupak Chatterjee  (8 years ago)

how is it i mean 25 15 and 9???

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tom  (8 years ago)

one side of biger cubes has 25 faces of smaller cube
bcoz 5*5
and totle 588faces (98*6)
(125-27=98)
total no of sml cube is 98cm3/1cm3=98
so 588-25=ans

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Tanveer Ray  (8 years ago)

can anyone explain the answer a little more vividly! 25*2+15*2+9*2 ??

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sreeja.R  (8 years ago)

please explain this question............

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bhushan dhande  (8 years ago)

563 is the right answer.....

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joydeb  (8 years ago)

3*3*3-2*2*2=98
98*6=588
588-4*25=
488

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Nimmi verma  (8 years ago)

Total no of cubes is 125 but this is hallow cube so total no of cube is 125-27=98 . 1 cube have 6 face . So total no of faces 98*6=588. Now 1 side is painted so 25 faces are already painted so total no unpainted faces are 588-25=563 is the ans.

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Golluru Lalitha  (8 years ago)

length of each side = 5cm + 2*1 cm=7cm
to make each cube of length of 1 cm we have to cut that cube into 7 smaller cubes
the unpainted smaller cubes= (7-2)^3 =125 [ .". (n-2)^3 ]

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Amanulla Khan  (8 years ago)

588-100=488

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Aditya Verma  (8 years ago)

corner cubes have 3 faces painted and 3 unpainted and 8 corners are there .so 8*3=24 faces
12 edges are there on which each is having 3 cubes whose 2 faces are painted and 4 are unpainted=4*12*3=144.
9 cubes are remaining on each face of big cube.so 1 painted and 5 unpainted in those faces=9*6*5=270
so total no. of unpainted faces are= 24+270+144=438

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Alisha  (8 years ago)

The Hallow cube volume = n3−(n−2)2, Here n is the number of small cubes lie on the big cube edge.
Now n = 5 so Hallow cube volume = 53−(5−2)2=125−27=98
So 98 small cubes required to make a hallow cube of size 5 cm. Now total surfaces = 6 x 98 = 588
Now if the bigger cube is painted 1 side, total 1 x 25 small faces got paint. So remaining small faces which does not have paint after cutting is 588 - 25 = 563

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