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Question

Select the dice which can be formed on folding the given sheet.

The correct answer is

To determine which dice can be formed by folding the given sheet, we need to understand the arrangement of the faces and how they relate to each other when folded. The given sheet is a net of a cube with the following layout:

In a typical die, opposite faces add up to seven. However, with the given sheet layout, we need to focus on the spatial arrangement:

  1. Face J is adjacent to F and E.
  2. Face F is adjacent to J, G, and E.
  3. Face G is adjacent to F and H.
  4. Face I is adjacent to H.

By understanding these adjacencies, we can eliminate options where supposedly adjacent faces are shown opposite each other in the given options. Let's evaluate each option:

    • In this option, the face arrangements conform to the net since the faces that should be adjacent are not opposite each other upon folding.
    • In this option, check if any adjacent faces from the sheet layout appear opposite. If two adjacent faces are opposite, this option is incorrect.
    • In this option, verify opposites for correctness. If any faces meant to be opposite appear adjacent, or vice versa, this configuration is incorrect.
    • Assess this option similarly to check adherence to spatial requirements from the net.

After careful evaluation, the correct answer is the first option. It maintains the structural integrity of adjacencies as outlined by the net.

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Important Questions from Cube and Dice

  1. A cube of side 80 cm is painted yellow on all the faces and then cut into smaller cubes of sides 8 cm each. Find the number of smaller cube having all the three faces painted.

  2. A cube of side 49 cm is painted purple on all the faces and then cut into smaller cubes of sides 7 cm each. Find the number of smaller cubes having only one face printed.

  3. A cube of side 18 cm is painted yellow on all the faces and then cut into smaller cubes of sides 3 cm each. Find the number of smaller cubes that have only two faces painted.

  4. A cube of side 12 cm is painted green on all the faces and then cut into smaller cubes of sides 2 cm each. Find the number of smaller cubes that have only one face painted.

  5. Four friends J, Q, B and Z rolled the dice in alphabetical order.

    The scores were:

    1st round: 3, 2, 5, 2

    2nd round: 1, 5, 1, 4

    3rd round: 4, 2, 1, 1

    If each point on the dice would get 10 points, who won the maximum points after 3 rounds?

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