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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
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
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 that are not
colored are 18*6=108
20 are two color face cubes so 20*4=80 faces are not colored
60 are one colored face so 60*5=300 faces are not colored.
so totally 108+80+300 faces are not colored
430
5x5x6 = 150 cube
150 – 20( corner cube) = 130 cube
130 x 3 (side remaining) = 390
20 x 2 (side remaining) = 40
total side remaining = 390 + 40 = 430