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 4 faces of the outer surface of the cube are painted, totally how many f

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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 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

900

500

488

800

Asked In TCS Neelkamal Sharma (12 years ago)

Solved Akash Read Solution (6)

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Read Solution (6) :

Akash  (12 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 (44) | No (1)  

Parul Patel  (12 years ago)

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

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

so, 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 = 98 / 1 = 98

Each cube has 6 faces, so 98 cubes have = 98*6 faces = 588

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

So, total unpainted faces = 588 - 100 = 488

Is this solution Helpfull? Yes (4) | No   

Diksha Kumari  (8 years ago)

How are you calculating size of hollow cube inside the big cube =3 cm, please elaborate

Is this solution Helpfull? Yes (2) | No   

Rajendra  (12 years ago)

small cubes in one side=5*5=25
Total small cubes=25*6=150

Two surface not painted so all faces
of small cubes=25*2*6=300

4 faces painted only one side=25*4*5=500

Total unpainted surface=500+300=800

Is this solution Helpfull? Yes | No (20)  

reena  (8 years ago)

how did u get each big side has 25 faces of the small cubes???

Is this solution Helpfull? Yes | No   

Subhagata Chakraborty  (8 years ago)

Reena each face of a cube is equivalent to a square. now the area of a square is square(side). thus we consider 4 such squares each with area 5*5=25.

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