GATE DA 2024 | Question 9

MCQ · 2 marks · −0.66

Three different views of a dice are shown in the figure below.

Three views of the same dice, each showing its top, left and right faces. View 1: 5 on top, 4 on the left, 1 on the right. View 2: 4 on top, 6 on the left, 3 on the right. View 3: 2 on top, 6 on the left, 5 on the right.

The piece of paper that can be folded to make this dice is

  1. Option A: Paper net of six squares: 5 and 1 side by side in the top row; below the 1, a column of 4 and then 6; below the 6, a bottom row of 2 with 3 to its right. (correct)
  2. Option B: Paper net of six squares: 5 and 1 side by side in the top row; below the 1, a column of 4 and then 2; below the 2, a bottom row of 6 with 3 to its right.
  3. Option C: Paper net of six squares: 5 and 1 side by side in the top row; below the 1, a column of 3 and then 2; below the 2, a bottom row of 4 with 6 to its right.
  4. Option D: Paper net of six squares: 5 and 1 side by side in the top row; below the 1, a column of 4 and then 6; below the 6, a bottom row of 3 with 2 to its right.

Answer

(A)

Explanation

Face 5 touches 4 and 1 (view 1) and 6 and 2 (view 3), so 3 is opposite 5. Face 4 touches 5 and 1 (view 1) and 6 and 3 (view 2), so 2 is opposite 4. That leaves 1 opposite 6.

In each net, the four squares of the vertical strip fold into a ring, so its 1st and 3rd squares are opposite, as are its 2nd and 4th; the two side squares are opposite too.

  • (A): 1–6, 4–2 and 5–3, all as required.
  • (B) and (C): 1 opposite 2, wrong.
  • (D): 4 opposite 3 and 5 opposite 2, wrong.

Folding (A) also shows each view’s three faces in the same clockwise order, so it makes this dice.

Answer: A