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1 mark

Which of the following cubes in the answer figures CANNOT be made on the basis of the unfolded cube in the question figure?

image

  1. A
    A
  2. B
    B
  3. C
    B
  4. D
    D

Solution & Step-by-step Explanation

By analyzing the unfolded cube, we can find the pairs of opposite faces because alternate faces are always opposite to each other:
1. The face with a single dot () is opposite to the face with the cross ().
2. The face with the star () is opposite to the face with four dots.
3. The face with two vertical parallel lines is opposite to the face with the hexagon ( -like shape).

According to the rules of dice, two opposite faces can never appear together on any visible view of a folded cube.

* Let's look at Option D: It shows the face with a single dot (), the face with four dots, and the face with a hexagon. Since none of these are opposite to each other, this cube can be made.
* Let's look at Option A: It shows the face with parallel lines, a single dot (), and a star (). These are all adjacent faces, so it can be made.
* Let's look at Option C: It shows the face with parallel lines, a cross (), and four dots. None of these are opposite pairs, so it can be made.
* Let's look at Option B: It shows the face with parallel lines and the face with a hexagon together as adjacent visible faces. Since these two faces are opposite to each other in the unfolded layout, they can never be seen together.

Therefore, the cube in Option B CANNOT be made.

Practice this question

Try it yourself before checking the explanation above.

Which of the following cubes in the answer figures CANNOT be made on the basis of the unfolded cube in the question figure?

image
A
A
B
B
C
B
D
D

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