Three different views of a dice are shown in the figure below. The piece of paper that can be folded to make this dice is
To determine the piece of paper that can be folded to make the dice shown in the images, we need to understand the relationship between the numbers on each face of the dice.
Let's analyze the different views of the dice:
- In the first view, faces with numbers 5, 4, and 1 are visible.
- In the second view, faces with numbers 4, 6, and 3 are visible.
- In the third view, faces with numbers 2, 6, and 5 are visible.
Now, we apply the rule: Two opposite faces of a dice cannot be adjacent in the views shown.
From the above views, we can conclude:
- Face 5 is adjacent to 4 and 1, but never opposite to them.
- Face 6 is adjacent to 4 and 3, indicating that 6 is opposite to 1 (since 1 is not visible in the second view).
- Face 2 is opposite to 4 (since 4 is not visible in the third view where 2 is seen).
Based on these observations, we identify the correct paper cutout for the dice from the given options. The cutout should have opposite faces not adjacent to each other:
Let's view the options given (please see images provided in the original question for visual reference):
This option shows arrangement where:
- 1 is opposite 6
- 2 is opposite 4
- 3 is opposite 5
This arrangement matches the conditions deduced from the views of the dice. Thus, the correct answer is:
Therefore, the piece of paper that can be folded to make this dice is the one indicated in the correct answer image above.
Important Questions from 2D 3D Pattern Visualization
- Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make?
An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The cylinder can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?
Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B.
If viewed from direction Y, the planar image of the assembly (Figure A) will appear asA palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.
From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome. The player should use all the five plates exactly once. The plates can be rotated in their plane.
The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.
What is the maximum number of squares without a "hole in the interior" that can be formed within the 4 × 4 grid using the unit squares as building blocks?
