## Cubes and Dice Question Figures

A cube is a 3 - dimensional solid object bounded by 6 sides, with three meeting at each vertex.

It features all right angles and a height, depth and width that are all equal ( length = height = width ).

It has two types: 1. Standard Cube; and 2. Non-Standard Cube

Important Facts:

I. A cube has 6 square facesor sides. (from Img 1)

II. A cube has 8 points (vertices). (from Img 1)

III. A cube has 12 edges. (from Img 1)

IV. Only 3 sides are visible at a time ["Joint Sides"] and

these joint sides can never be on opposite side to each other.

V. Things that are shaped like a cube are often referred to

as ‘cubic’.

VI. Most dice are cube shaped, featuring the numbers 1 to 6

on the different faces.

VII. Addition of number of dots (pips) or numbers from opposite sides of a standard cube or dice

is always 7.

VIII. Total of 2 adjacent faces of cube can never be a 7.

IX. 11 different ‘nets’ can be made by folding out the 6 square faces of a cube. (from Img 2)

:: Problem Solving ::

Things to remember before stepping ahead:

* We can categorise a cube (or a colour cube) after cutting it, in these four categories: (See img 3)

I.) Central cube (Yellow): In middle of faces & has only one coloured side.

We can find out the total number of cubes with singe color on any side with this formula:

6(X-2)2

II.) Middle Cube (Green): In middle of edges and have two coloured sides.

We can find out the total number of cubes with singe color on any side with this formula:

12(X-2)

III.) Corner cube (Blue): Cubes on corners and have 3 coloured sides.

A cube can have only 8 cut-corner cubes with colors on three sides.

Hence answer will be always the same - 8.

IV.) Inner Cube (No Color): Cubes inside faces and has no coloured side.

We can find out the total number of cubes without any color on any side (inner cube) with this formula: (X-2)3

***Note: To find out total number of cubes we use this formula - (X)3

Question Type 1 : Determining the opposite sides

Question Type 2 : Cutting a Colorful Cube

Question Type 3 : Making big cube by adding small cubes

Question Type 4 : Determining number of cubes placed in stacks

Examples: Question Type 1

• This cube is a 'standard cube'. What will be the number on opposite faces of it?

1. Opposite to 1 - ?

2. Opposite to 2 - ?

3. Opposite to 3 - ?
• Solution:

We know rule of standard cube - 'Addition of number of dots (pips) or numbers from

opposite sides of a standard cube or dice is always 7'

the rule = 7-N (N stands for number on

facing side).

I. Opposite to 1 = (7-1) = 6

II. Opposite to 2 = (7-2) = 5

III. Opposite to 3 = (7-3) = 4
•
• 2. Study these cubes and find out the numbers on opposite sides of front facing sides of these.

•
• Solution:

To solve this question we'll follow this rule - 'Only 3 sides are visible at a time (called "Joint Sides")

and these joint sides can never be on opposite side to each other.'

1. From cube A and B - 1, 2, 3, 4 and 5 can never be on opposite side of 3 (common number in cube A and B).

Hence the answer will be = 6

2. From cube B and C - 1, 3, 4, 6, and 5 can never be on opposite side of 5

(common number in cube B and C).

the answer will be = 2

3. From cube A and C - 1, 2, 3, 5 and 6 can never be on opposite side of 1

(common number in cube A and C).

the answer will be = 4

Conclusion :

Opposite to 1 = 4

Opposite to 3 = 6

Opposite to 5 = 2

To whom this Cubes and Dice Question Figures section is beneficial?

Students can learn and improve on their skillset for using Verbal Ability effectively and can also prepare for competitive examinations like...

• All I.B.P.S and Public Sector Bank Competitive Exam
• Common Aptitude Test (CAT) Exams
• UPSC Paper-II or CSAT Exams
• SSC Competitive Exams
• Defence Competitive Exams
• L.I.C / G.I.C AAO and Clerk Competitive Exams
• Railway Competitive Exam
• University Grants Commission (UGC)
• Career Aptitude Test (IT Companies) and etc.