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How many dots lie opposite to the face having three dots, when the given figure is folded to form a cube?

 

  • Option 1)

     

    3

     

  • Option 2)

     

    4

     

  • Option 3)

     

    5

     

  • Option 4)

     

    6

     

  • Option 5)

     

    2

     

Opposite 3 dots = 6 dots

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Choose the box that is similar to the box formed from the given sheet of paper (X).

 

  • Option 1)

     

    1 and 4 only

     

  • Option 2)

     

    3 and 4 only

     

  • Option 3)

     

    1 and 2 only

     

  • Option 4)

     

    None of these

     

  • Option 5)

     

    2 and 3 only

     

the above diagram is showing faces & their opposite faces. We know that in a 3D view of dice, 1. Each faces out three faces in 3D view should be from all pair. 2. Two opposite faces cannot come in any 3D view. As per the above diagram & rules, Only 1 & 4 can be crafted.

 

Choose the box that is similar to the box formed from the given sheet of paper (X).

 

  • Option 1)

     

    1 and 2 only

     

  • Option 2)

     

    None of these

     

  • Option 3)

     

    2 and 3 only

     

  • Option 4)

     

    1 and 4 only

     

  • Option 5)

     

    2 and 4 only

     

the above diagram is showing faces & their opposite faces. We know that in a 3D view of dice, 1. Each faces out three faces in 3D view should be from all pair. 2. Two opposite faces cannot come in any 3D view. As per the above diagram & rules, Only 2 & 3 can be crafted.

 

What is the least number of cuts required to divide a cube into 125 identical pieces?

 

  • Option 1)

     

    6

     

  • Option 2)

     

    8

     

  • Option 3)

     

    10

     

  • Option 4)

     

    12

     

  • Option 5)

     

    15

     

125 = 5 x 5 x 5 So number of cuts = 4 + 4 + 4 => 12

 

Each face of a cube is painted either white or black. In how many ways can a cube be painted?

 

  • Option 1)

     

    8

     

  • Option 2)

     

    10

     

  • Option 3)

     

    11

     

  • Option 4)

     

    16

     

  • Option 5)

     

    12

     

Number of ways in which four faces can be painted = 24 => 16

 

What is the maximum number of identical pieces a cube can cut into by 5 cuts?

 

  • Option 1)

     

    29

     

  • Option 2)

     

    20

     

  • Option 3)

     

    18

     

  • Option 4)

     

    16

     

  • Option 5)

     

    25

     

Making pair of three out of 5 cuts = (1, 2, 2) Number of Cubes = (1 + 1)(2 + 1)(2 + 1) => 2 x 3 x 3 => 18

 

What is the maximum number of identical pieces a cube can cut into by 4 cuts?

 

  • Option 1)

     

    10

     

  • Option 2)

     

    12

     

  • Option 3)

     

    18

     

  • Option 4)

     

    5

     

  • Option 5)

     

    16

     

If 4 cuts made on a cube, So the number of possible cube through 3 cuts = 24 => 16

 

What is the maximum number of identical pieces a cube can cut into by 3 cuts?

 

  • Option 1)

     

    9

     

  • Option 2)

     

    8

     

  • Option 3)

     

    4

     

  • Option 4)

     

    6

     

  • Option 5)

     

    7

     

If 3 cuts made on a cube, So the number of possible cube through 3 cuts = 23 => 8
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