Choose the box that is similar to the box formed from the given sheet of paper (X).
Options
A. 1 and 3 only
B. 2, 3 and 4 only
C. 2 only
D. 3 and 4 only
Correct Answer
2 only
Explanation
The fig. (X) is similar to the
Form I. So, when the sheet in fig. (X) is folded to form a cube, then the completely shaded face lies opposite to the half shaded face. Therefore, the cubes shown in figures (1) and (3) which have the completely shaded face adjacent to the half-shaded face cannot be formed. Since Fig 4 does't have at-least one shaded face, it cannot be formed. Hence, only the cubes in figure (2) can be formed.
Cubes and Dice problems
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1. Choose the box that is similar to the box formed from the given sheet of paper (X).
The fig. (X) is similar to the
Form VI. So, when a cube is formed by folding the sheet shown in fig. (X), then
is one of the faces of the cube and this face lies opposite to a blank face. Also, a face bearing a circle lies opposite to one bearing a dot. Clearly, this cube does not have faces as shown in the cubes in figures (3) and (4). Hence, only the cubes shown in figures (1) and (2) can be formed.
2. Choose the box that is similar to the box formed from the given sheet of paper (X).
The fig. (X) is similar to the
Form VII. So, when a cube is formed by folding the sheet shown in fig. (X), then
is one of the faces of the cube and this face lies opposite to a blank face. Also, a face bearing a square lies opposite to another blank face. The remaining two blank faces lie opposite to each other. Clearly, in the cube shown in fig. (1), the face consisting of the four symbols is not the same as that formed (as shown above). Hence, the cube in fig. (1) cannot be formed.
3. Choose the box that is similar to the box formed from the given sheet of paper (X).
The fig. (X) is similar to the
Form V. So, when the sheet in fig. (X) is folded to form a cube, then the face bearing a dot lies opposite to one of the shaded faces. Therefore, the cube shown in fig. (2) which has both the shaded faces adjacent to the face bearing the dot, cannot be formed. Hence, the cubes shown in figures (1), (2) and (4) can be formed.
4. Choose the box that is similar to the box formed from the given sheet of paper (X).
The fig. (X) is similar to the
Form II. So, when the sheet shown in fig. (X) is folded to form a cube then the two half-shaded faces lie opposite to each other, the face bearing a square lies opposite to one of the two blank faces and the face bearing a circle lies opposite to the other blank face. Therefore, the cubes shown in figures (2) and (3) which have the two half-shaded faces adjacent to each other, cannot be formed by folding the sheet shown in fig. (X). Also, though the cube shown in fig. (4) has faces that can appear adjacent to each other but the cube formed by folding the sheet in fig. (X) cannot be rotated to form the cube in fig. (4). Hence, only the cube in fig. (1) can be formed.
5. Choose the box that is similar to the box formed from the given sheet of paper (X).
The fig. (X) is similar to the
Form III. So, when the sheet in fig. (X) is folded to form a cube, then the half-shaded face appears opposite to the face bearing a rhombus, the face with a black circle appears opposite to one of the two blank faces and the face with a '+' sign appears opposite to the other blank face. Clearly, the cubes shown in figures (1) and (4) cannot be formed since they have the half-shaded face adjacent to the face bearing the rhombus. Also, though the cube shown in fig. (3) has faces that can appear adjacent to each other but the cube formed by folding the sheet in fig. (X) cannot be rotated to form fig. (3). Hence, the cube in fig. (3) cannot be formed. Thus, only the cube shown in fig. (2) can be formed.
6. Choose the box that is similar to the box formed from the given sheet of paper (X).
The fig. (X) is similar to the
Form V. So, when the sheet shown in fig. (X) is folded to form a cube then the shaded face lies opposite to one of the blank faces, the face bearing a circle lies opposite to another blank face and the face bearing a shaded square lies opposite to the third blank face. Thus, each one of the cubes shown in figures (1), (2) and (4) can be formed. Also, though the cube shown in fig. (3) has faces that can appear adjacent to each other but the cube formed by folding the sheet in fig. (X) cannot be rotated to form fig. (3). Hence, the cube in fig.(3) cannot be formed.
7. Choose the box that is similar to the box formed from the given sheet of paper (X).
The fig. (X) is similar to the
Form V. So, when the sheet in fig. (X) is folded to form a cube, then the face bearing a square lies opposite to the face bearing a circle. Therefore, the cubes shown in figures (1) and (2) which have the faces bearing the square and the circle adjacent to each other, cannot be formed. Hence, only the cubes in figures (3) and (4) can be formed.
8. Choose the box that is similar to the box formed from the given sheet of paper (X).
The fig. (X) is similar to
Form V. So, when the sheet shown in fig. (X) is folded to form a cube, then the face with shading lies opposite to the free bearing a square, the face bearing a dot lies opposite to a blank face and the face bearing a circle (with a '+' sign inside it) lies opposite to another blank face. The cubes in figures (2) and (4) have the shaded face adjacent to the face bearing a square. Therefore, the cubes in these two figures cannot be formed. Hence, only cubes in figures (1) and (3) can be formed.
9. Which of the following finished patterns can be obtained from the piece of cardboard (X) shown below?
The fig. (X) is similar to
Form I. So, when the sheet shown in fig. (X) is folded to form a box (cuboid), then the two rectangular-shaded faces lie opposite to each other, two rectangular white faces lie opposite to each other and the two square shaped faces (one shaded and one white) lie opposite to each other. Clearly, the cuboids shown in figures (2) and (4) cannot be formed as in each of the two cuboids the two shaded rectangular faces appear adjacent to each other. So, only the cuboids in figures (1) and (3) can be formed.