6th Class Mental Ability Related to Competitive Exam Cubes and Dice

Cuboid:

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

Cube:

Cube is a cuboid which has 6 square faces, 8 corners and 12 edges.

Dice:

A dice is a cube which contains 6 different numbers on its 6 faces.

EXAMPLE

1.         Count the number of blocks in the given solid.

               (a) 24                            (b) 36                            (c) 48                            (d) 60

Explanation (b):

Each layer (say top most) of the solid contains 12 blocks.                                         

There are 3 identical layers in all.                      

So, the total number of blocks

2.         Two positions of a dice are shown below. How many dots will appear on the face opposite to the face containing 5 dots?

              (a) 3                              (b) 1                              (c) 2                              (d) 4

Explanation (d):

From two positions, we observe that 4 dots are on the common adjacent face of dots 2 & 1.

Hence, 4 dots are opposite to 5 dots.

3.         A sheet of paper shown in the figure (X), is folded to form a box. Choose a box from the options that is similar to the box given in fig. (X).

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

Explanation (d):

Considering the positions of faces on forming a box, we deduce that the pairs of opposite faces are:

These three pairs of opposite faces are possible in all the boxes 1, 2, 3 and 4.