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A hollow cube of size 5cm is taken , with the thickness
of 1cm . it is made of smaller cubes of size 1cm . if the
outer surface of the cube is painted how many faces of the
smaller cubes remain unpainted?
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Answer / subraj
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 Answer Correct ? | 217 Yes | 31 No |
Answer / sinha
The above answer would be correct if the question would be that 4 sides are painted, BUT here its given all the sides are painted of the bigger cube..
So, no of painted faces = 25*6 = 150 (and not 25*4=100)
so answer here would be :-
588-150 = 438
| Is This Answer Correct ? | 46 Yes | 21 No |
Answer / anni
Answer:: is 488.how this is
first take 5 cm cube so its volume is 5^3=125
and it is hallow of 1 cm thickness so the inner cube has 3cm
edge
so its volume is 27
subtraction 125-27=98
so 98 1cm cubes can be made
in those 98
18 are no color face cubes so no of faces which are not
coloured are 18*6=108
20 are two color face cubes so 20*4=80 faces are not coloured
60 are one colored faces so 60*5=300 faces are not coloured.
so totally 108+80+300 faces are not colored
| Is This Answer Correct ? | 10 Yes | 8 No |
Answer / satheesh
total number of smaller cubes of size 1cm = 98
out of these 98 cubes,
since four sides r painted
9*4 -> painted on 1 side.... 36*5 = 180 unpainted faces
5*4 -> painted on 2 sides... 20 * 4 = 80 unpainted faces
no-> painted on 3 sides
total = 180+80= 260 unpainted faces..
| Is This Answer Correct ? | 6 Yes | 33 No |
Answer / shyam
total number of smaller cubes of size 1cm = 98
out of these 98 cubes,
54 -> painted on 1 side.... 54*5 = 270 unpainted faces
36 -> painted on 2 sides... 36 * 4 = 144 unpainted faces
8 -> painted on 3 sides... 8 * 3 = 24 unpainted faces
total = 270 + 144 + 24 = 438 unpainted faces..
| Is This Answer Correct ? | 22 Yes | 53 No |
Answer / sandeepb
total small cubes formed=125
no of faces of all small cubes=125*6=750
original cube is painted
on each face of orginal cube 5*4=25 faces of small cube
so total faces painted=25*6=150
unpainted faces=750-150=600
| Is This Answer Correct ? | 32 Yes | 65 No |
Answer / brett
Total number of small cubes = 86
Total number of faces = 86x6 = 516
Painted faces on each side of large cube = 25
Total painted faces = 25x6 = 150
Number of unpainted faces = total faces - painted faces
Number of unpainted faces = 516-150 = 366
| Is This Answer Correct ? | 2 Yes | 47 No |
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