**Cube**

Most of the aptitude exam have consist of this kind of dice
problems. Here we will discuss methods to solve such problems but before that
let have a look on CUBE

· It has 6
sides/faces , 8 corners and 12 edges.

· Length of
all the side are equal

· If x be the
length of side then,

o
Area of all surfaces = 6x

^{2}
o
Volume = x

^{3}
· When a
bigger cube is cut in

**N**equal small size cube then**Area of Bigger Cube = N× Area of Smaller Cube**
Let’s understand with an example

A cube is painted
blue on all the faces. Then cut into 27 cubes of equal size. Length of side of
bigger cube is 6 m.

**Area of Bigger Cube = N× Area of Smaller Cube**

=

**125× Area of Smaller Cube****5**

^{3}= 125×X^{3}**Size of smaller cube X = 1**

Since the side of smaller cube is
1/ 5

^{th}side of larger cube , hence there would be five layers of smaller cubes.__Observations:__

In each layer :

9
middle cubes painted only one face

4
cubes at the corner painted three face

Remaining
12 cubes painted 2 faces.

In three middle layers:

9
middle cubes painted no color

4
cubes at the corner painted two color

Remaining
12 cubes are painted one face

__Formulas :__**For Number of layer = n**

^{· }No of cubes painted no color = (n-2)

^{3}

·
No
of cubes painted only one face = (n-2)

^{2}×6
·
No
of cubes painted only two faces = (n-2)× 12

·
No
of cubes painted three faces = 8(corner cubes only)

·
No
of cubes painted only one face = (n-2)

^{2}×6**Dice**

In these types of problem some different positions
of a DICE would be given, based on that we are ask to find the numbering on
different faces.

Example:

**From the positions of a cube are shown below, Which letter will be on the face opposite to face with '1'?**

Explanation:

Adjacent to 1 are 2,6,3,5

5 and 6 are on the opposite face.

Only number remains is 4.

Hence the number opposite to the face of 1 would be 4