7th Class Mental Ability Related to Competitive Exam Cubes and Dice

Cuboid: Cuboid is a uniform solid which has 6 faces, 8 corners and 12 edges.

Cube: Cube is a cuboid which has identical faces.

Dice: A dice is a cube whose each face contains dots or numbers from 1 to 6.

EXAMPLE

1.  Count the number of cubes in the given figure.

(a) 8                              (b) 10                            (c) 12                            (d) 16

Explanation (b):

Number of cubes in the bottom layer = 6

Number of cubes in the middle layer = 3

Number of cubes in the topmost layer = 1

 Total number of cubes

So, the correct option is (b).

2.  Study the two positions of a dice given below. What number will be opposite to the face bearing number 2?

(a) 4                              (b) 3                              (c) 6                              (d) 5

Explanation (d):

First figure shows that faces bearing 1 and 3 are adjacent faces of the face bearing 2. So they cannot be opposite to 2.

From second figure:

3 is on the top. So 2 cannot be at the bottom.

1 is at the front. So 2 cannot be at the back.

Clearly, only one face of this (2nd figure) dice is remaining. Hence it must be 2.

Therefore, 5 is opposite to 2.

So, the correct option is (d).

3.  The sheet of paper shown in the fig. (X), is folded to form a box. Choose box(es) from the options, that is similar to the box(es) that are formed.

       (a) 2 and 3 only              (b) 1, 3 and 4 only          (c) 1, 2 and 3 only          (d) 1 and 4 only

Explanation (c):

After folding the fig. (X), we get the box whose opposite faces are:

No rotation of the box is formed appears as shown in the figure 4.

So, the correct option is (c).