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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 Posted / 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 |
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