8th 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 6 identical faces.

Dice:

A dice is a cube whose each face bears points or numbers from 1 to 6.

EXAMPLE

Count the number of cubes in the following figure.

       (a) 28                            (b) 32   

       (c) 36                            (d) 40

Explanation (a) :

Number of cubes in the bottom layer = 5

Number of cubes in the next layer = 8.

Number of cubes in the next layer = 9

Number of cubes in the topmost layer = 6

\[\therefore \] Total number of cubes =5+8+9+6= 28

2. Here two positions of a dice are shown. If there are four dots in the bottom, then how many dots will be on the top?

     (a) 2                              (b) 3              

     (c) 5                              (d) 6

Explanation (b) :

A student requires here the number of points opposite four points.

Four points are showing in both the positions of dice.

So none of 1 point, 2 points, 5 points and 6 points is opposite to 4 points.

Therefore the required number of points is 3.

So the correct option is (b).

3.  A solid cube of each side 8 cm has been painted on all the faces. It is then cut into cubical blocks of each side 2 cm. How many cubes have only two faces painted?

    (a) 4                              (b) 8               

   (c) 24                            (d) 32

Explanation (c):

Number of cubes each having only two faces painted are on each 12 edges.

Therefore number of cubes having two faces painted is 24.

4.   The sheet of paper shown in the figure (X). Choose a box from the four options that is similar to the box that formed.

         (a)                (b)  

         (c)                 (d)  

Explanation (d):

Opposite pair of faces are:

after folding the sheet, we get a box as shown in option (d).