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Direction : A cuboid is divided into 192 identical cubelets This Is done by making minimum no. ot cuts possible. At cuts are parallel to some of the face. But before that, The cube is-painted with green color on one set of opposite faces. Blue on other set of opposite faces and tea on their pair of annosit faces.
Q. What is the number of cubelets possible which are painted with none of the color?
  • a)
    16
  • b)
    24
  • c)
    36
  • d)
    48
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Direction : A cuboid is divided into 192 identical cubelets This Is d...
Number of unpainted cubelets will be (4 - 2) x (6 - 2) x (8 - 2) = 2 x 4 x 6 = 48
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Direction : A cuboid is divided into 192 identical cubelets This Is d...
Solution:

Given, a cuboid is divided into 192 identical cubelets by making minimum cuts possible. The cuts are parallel to some of the face. Before cutting the cube, it is painted with green color on one set of opposite faces, blue on the other set of opposite faces, and tea on their pair of adjacent faces.

We need to find the number of cubelets that are painted with none of the colors.

Let's analyze the given information to find the solution.

Total number of cubelets = 192

Each face of the cuboid is divided into 8 cubelets.

The number of cubelets with green color = Number of cubelets on the opposite faces painted with green color = 8 x 6 = 48

Similarly, the number of cubelets with blue color = Number of cubelets on the opposite faces painted with blue color = 8 x 6 = 48

The number of cubelets with tea color = Number of cubelets on adjacent faces painted with tea color = 8 x 4 = 32

Now, the number of cubelets that are painted with none of the colors can be found by subtracting the total number of painted cubelets from the total number of cubelets.

Number of cubelets that are painted with none of the colors = Total number of cubelets - (Number of cubelets with green color + Number of cubelets with blue color + Number of cubelets with tea color)

Number of cubelets that are painted with none of the colors = 192 - (48 + 48 + 32) = 64

Hence, the correct option is (d) 48.
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Direction : A cuboid is divided into 192 identical cubelets This Is done by making minimum no. ot cuts possible. At cuts are parallel to some of the face. But before that, The cube is-painted with green color on one set of opposite faces. Blue on other set of opposite faces and tea on their pair of annosit faces.Q. What is the number of cubelets possible which are painted with none of the color?a)16b)24c)36d)48Correct answer is option 'D'. Can you explain this answer?
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