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

• Placement Papers
• /
• TCS
• /
• Numerical Ability
• /
• Geometry

TCS Question Papers: TCS Interview Experience(90) TCS Company Profile

(#M40040429) TCS Numerical Ability question Keep an EYE

a hollow cube of size 5 cm is taken of thickness 1 cm. it is made of smaller cubes of 1 cm. if 1 face of outer surface of the cube are painted. find how many total faces of the smaller cube remain unpainted

Asked In TCS Ruchi Sehgal (9 years ago)

Unsolved Read Solution (8)

Is this Puzzle helpful?   (0)   (0) Submit Your Solution Geometry

Read Solution (8) :

Anuj Yadav  (9 years ago)

Total number of small cubes=98
Total number of faces 98*6=588

Now one face of outer cube is painted hence 25 faces got painted
=> total faces of small cube remain unpainted=588-25=563

Hence answer is 563

Correct me if I am wrong

Is this solution Helpfull? Yes (10) | No (3)  

RABI KR. SHAW  (9 years ago)

hollow cube volume=n^3 - (n-2)^2
n > no of small cubes
n=5 > 5^3-(5-2)^2=98
i.e. 98 small cubes
total surfaces = 6*98=588
if bigger cube is painted 4 sides i.e. 4*25=100 small faces got paint
face does not paint=588-100=488

Is this solution Helpfull? Yes (6) | No (3)  

satyam  (9 years ago)

Volume of Big Cube considering it is not hollow = L^3 = 5*5*5 = 125 cm^3
Size of hollow cube (considering 1 cm thickness on two faces of large cube = 5-2 = 3cm
Volume of hollow cube = 3*3*3 = 27 cm^3

So Total Volume filled up by smaller cubes = Volume of Larger Cube - Volume of hollow cube = 125 - 27 = 98 cm^3
Volume of 1 small cube = 1*1*1 = 1 cm^3
Total number of small cubes in the larger cube = 98/1 = 98
and Number of faces of 98 small cubes (6 faces each cube has) = 98*6 = 588 faces

Total Surface area of 6 faces of larger cube painted = 6*L^2 = 6*5*5 = 150cm^2
Surface area of one face of small cube = 1*1 = 1cm^2
Number of faces of small cube painted = 150/1 = 150 faces

=> Hence number of faces of the smaller cubes remain unpainted = 588-150 = 438

Is this solution Helpfull? Yes (6) | No   

jhansi  (9 years ago)

total small cubes required is 5^3-3^3=588
1face of outer surface of cube is painted=so small 25 are required for that
unpainted small cubes is 588-25=563

Is this solution Helpfull? Yes (5) | No (2)  

syed fayaz  (9 years ago)

ans : 488

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

aru  (9 years ago)

475 faces of smaller cubes remain unpainted.

Is this solution Helpfull? Yes | No (1)  

DHIRAJ KUMAR  (9 years ago)

total small cubes required is 5^3-3^3=588
1face of outer surface of cube is painted=so small (25-9) are required for that
unpainted small cubes is 588-16=572

Is this solution Helpfull? Yes | No   

Ayush Upadhyaya  (9 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

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.