Latest TCS Aptitude Question SOLUTION: A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 1 face of the outer surface of the cube are painted, totally how many f

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(#M40000999) TCS Logical Reasoning question Keep an EYE

A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 1 face of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
a) 900 b) 488 c) 563 d) 800

Asked In TCS Anil (13 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

suresh  (11 years ago)

The big cube is completely hollow.. But, the thickness of
its side is 1cm & this is made up of smaller cubes.

Just like the walls of a room. The room is hollow, but, its
thickness is due to smaller bricks. The 4 walls of this room
is painted from the outside. And, you are asked totally how
many sides of all the bricks are now unpainted.

First, you need to know how many bricks (small cubes) are there.

Size of big cube = 5cm
Total volume of the big cube = 5*5*5 = 125cm^3

Size of the hollow cube inside the big cube = 3cm
Volume of the hollow space inside the big cube = 3*3*3 = 27cm^3

Therefore, volume occupied by small cubes (or volume of
thickness) = 125 - 27 = 98cm^3

Size of each small cube = 1cm
Volume of each small cube = 1*1*1 = 1cm^3
Total number of small cubes in wall = 98 / 1 = 98

In short, 98 small cubes make up the wall of the big cube.
Each cube has 6 faces, so 98 cubes have = 98*6 faces = 588

The four sides of the big cube have 100 painted faces.
Because each big side has 25 faces of the small cubes.

Therefore, total unpainted faces = 588 - 100 = 488

Is this solution Helpfull? Yes (114) | No (16)  

RISHI KUMAR  (13 years ago)

total number of blocks=(5*5*5)-(3*3*3)=98
so total no of faces of smaller cubes=98*6=588
and among all these faces one face of bigger cube is painted so totally 25 faces of small cubes r painted
it means total unpainted faces=588-25=563 (c)

Is this solution Helpfull? Yes (89) | No (61)  

mahadev  (13 years ago)

total no of cubes in solid cube =5^3
total no of cubes in given hollow cube = 5^3-3^3=98
total no of faces =98*6=588
total faces painted = 25*4=100
therefore faces unpainted =588-100=488

Is this solution Helpfull? Yes (47) | No (36)  

kamran  (13 years ago)

answer is 563
no of cubes of 1cm size is
5^3-3^3=98
no of faces 98*6=588
if one side is painted then 5*5=25 surfaces is paintedremaining are unpainted..
so 588-25=563

Is this solution Helpfull? Yes (14) | No (15)  

mahadev  (13 years ago)

total no of cubes in solid cube =5^3
total no of cubes in given hollow cube = 5^3-3^3=98
total no of faces =98*6=588
since one face of big cube painted total faces painted = 25
therefore faces unpainted =588-25=563

Is this solution Helpfull? Yes (12) | No (13)  

Praveen J  (12 years ago)

hello mahadev,
can u explain why you have 5^3-3^3.
the 3^3 how comes? please explain briefly

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

Somil Nain  (13 years ago)

488
for detailed solution see previous pages

Is this solution Helpfull? Yes (1) | No (19)  

chandan mishra  (10 years ago)

plzz explain rishi

Is this solution Helpfull? Yes (1) | No   

arnab sanyal  (9 years ago)

the formula is {(n^3-(n-2)^3)*6}-(no of faces painted * n^2) here n=5 and no of faces painted =1 so putting the value the ans is =563

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

ramesh chandi  (9 years ago)

answer is 563
588-25=563

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

RISHABH  (9 years ago)

total no of cubes in solid cube =5^3
total no of cubes in given hollow cube = 5^3-3^3=98
total no of faces =98*6=588
since one face of big cube painted total faces painted = 25
therefore faces unpainted =588-25=563

Is this solution Helpfull? Yes | No (2)  

kiruthika ganesan  (4 years ago)

488
x=5;
t=1,s=1

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