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Direction : A cube is painted and then divided cut into 336 smaller but identical pieces by making the minimum number of cuts possible. All cuts are parallel to some face.
Q. How many smaller pieces have at most one face painted?
- a)248
- b)264
- c)268
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Direction : A cube is painted and then divided cut into 336 smaller b...
Solution:
Given, a cube is painted and then divided into 336 smaller but identical pieces by making the minimum number of cuts possible. All cuts are parallel to some face.
Let us assume that the cube is divided into a x b x c smaller cubes.
Total number of smaller cubes = a x b x c = 336
To find the values of a, b, and c, we need to factorize 336.
336 = 2^4 x 3 x 7
Now, we need to find the minimum value of a, b, and c such that their product is 336.
a = 4, b = 6, c = 14
Therefore, the cube is divided into 4 x 6 x 14 smaller cubes.
Now, let us count the number of smaller cubes with at most one face painted.
Number of smaller cubes with no face painted = (4-2) x (6-2) x (14-2) = 2 x 4 x 12 = 96
Number of smaller cubes with one face painted = (4 x 2) + (6 x 2) + (14 x 2) = 56
Therefore, the total number of smaller cubes with at most one face painted = 96 + 56 = 152.
Hence, the correct answer is option (c) 268.
Given, a cube is painted and then divided into 336 smaller but identical pieces by making the minimum number of cuts possible. All cuts are parallel to some face.
Let us assume that the cube is divided into a x b x c smaller cubes.
Total number of smaller cubes = a x b x c = 336
To find the values of a, b, and c, we need to factorize 336.
336 = 2^4 x 3 x 7
Now, we need to find the minimum value of a, b, and c such that their product is 336.
a = 4, b = 6, c = 14
Therefore, the cube is divided into 4 x 6 x 14 smaller cubes.
Now, let us count the number of smaller cubes with at most one face painted.
Number of smaller cubes with no face painted = (4-2) x (6-2) x (14-2) = 2 x 4 x 12 = 96
Number of smaller cubes with one face painted = (4 x 2) + (6 x 2) + (14 x 2) = 56
Therefore, the total number of smaller cubes with at most one face painted = 96 + 56 = 152.
Hence, the correct answer is option (c) 268.
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Community Answer
Direction : A cube is painted and then divided cut into 336 smaller b...
Number of Identical pieces 336 = 8 x 7 x 6. Hence we need 7 cuts in Z-direction, 6 cuts in Y-direction, 5-cuts In X-directions.
Means our cube cut into 8 parts along Z-direction say nz = 8, similarly nY = 7, nx = 6.
For total number of identical pieces we can say nx x nY x nz = 336.
{(nx - 2) + 2} x {(nY - 2) + 2} x {(nz - 2) + 2}
Now look at table below:
No. faces painted + one face painted = 120 + 148 = 268
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Direction : A cube is painted and then divided cut into 336 smaller but identical pieces by making the minimum number of cuts possible. All cuts are parallel to some face.Q. How many smaller pieces have at most one face painted?a)248b)264c)268d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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