Cube and Dice MCQ Quiz - Objective Question with Answer for Cube and Dice - Download Free PDF

Opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surface are touched by side or by corners

So, by using the above rule we can find the opposite surface of open dice.

In the given figure, Opposite faces are :

(1)  →  None of the opposite faces are seen together nor they are adjacent to each other so, This cube can be formed.

(2)→ Opposite faces are seen together so, this cube cannot be formed.

(3)→ Opposite faces are seen together so, this cube cannot be formed.

(4) → Opposite faces are seen together so, this cube cannot be formed.

Hence, the correct answer is "Option (1)".

The faces opposite to each other is shown below:

The opposite sides are:

1)  → This cube can be formed as no two opposite faces appear together on the same dice. 

2)  → This cube cannot be formed as  and faces are opposite faces and no two opposite faces can appear together on the same dice. So, this cube can't be formed.

3)  → This cube cannot be formed as  and faces are opposite faces and no two opposite faces can appear together on the same dice. So, this cube can't be formed.

4)  → This cube cannot be formed as  and faces are opposite faces and no two opposite faces can appear together on the same dice. So, this cube can't be formed.

Hence, ‘option 1’ is the correct answer.

From the given figures:

Opposite faces are:

KC ⇔ OC

DC ⇔ CA

AC ⇔ GC

Here, the opposite face of OC is KC.

Hence, the correct answer is "KC".

Opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surface are touched by side or by corners

The opposite faces are:

Option 1: cannot be formed, since opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

Option 2: cannot be formed since opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

Option 3: can be formed since none of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

Option 4: cannot be formed as to make cube two concentric circles should be replaced by star.

Hence, cube given in option 3 can be made from the given sheet of paper.

@ is there in the1^st dice. In order to find the face opposite to @, take 1^st and 3^rd dice. # is common in both the faces. Keeping the face ‘#’ constant, and then rotating in the clockwise direction, we find the faces opposite to each other.

For find the adjacent faces of '4', we need to compare the common surface in the given dices,

Now,

From Dice 2 and Dice 3,

Here, 3, 5, and 6 is the adjacent surfaces of 4.

So, according to the options '6 and 5' will be the adjacent surfaces of 4.

Hence, the correct answer is "Option 4".

Given:

Length of the side of the big cube = 125 cm.

Length of the side of the smaller cube = 25 cm.

Formula:

A cube is a three-dimensional figure with 8 corners, 6 surfaces, and 12 edges (sides).

If a cube is painted on all of its surfaces with the same colour, and then divided into smaller cubes of equal size, then the number of smaller cubes so obtained will be calculated as follows:

• Number of cubes with no face painted = (n - 2)³
• Number of cubes with one face painted = 6(n - 2)²
• Number of cubes with two faces painted = 12(n - 2)
• Number of cubes with three faces painted = 8(Always)

 where n = No. of parts of each side = Length of the side of larger cube ÷ length of the side of the smaller cube

Calculation:

n = 125 ÷ 25 = 5

⇒ n - 2 = 3

Number of smaller cubes having at least two faces painted

= total no. of cubes - (no. of cubes with no face painted + no. of cubes with only one face painted)

= 125 - (3³ + 6 × 3²)

= 125 - (27 + 54)

= 125 - 81

= 44

Hence, 44 is the correct answer.

From the given dice:

L is the common letter in both Dice,

So, 7 is the opposite surface of 8.

and, F and 9 is the opposite surface.

Therefore, among the given options, 8 and L will be the adjacent surface of 'F'.

Hence, the correct answer is "Option 1".

Logic : (Cube of 1st number + Cube of 3rd number) / 2 = 2nd number

Given :

• (3, 14, 1)

⇒\({(3)^3 + (1)^3 \over 2}\) = 14

⇒\({27 + 1 \over 2}\) = 14

⇒\({28 \over 2}\) = 14

⇒14 = 14 (LHS = RHS)

• (4, 36, 2)​

⇒\({(4)^3 + (2)^3 \over 2}\) = 36

⇒\({64 + 8 \over 2}\) = 36

⇒\({72 \over 2}\) = 36

⇒36 = 36 (LHS = RHS)

So,

• Option - (1) : (8, 12, 2)​

⇒\({(8)^3 + (2)^3 \over 2}\) = 12

⇒\({512 + 8 \over 2}\) = 12

⇒\({520 \over 2}\) = 12

⇒260 ≠ 12 (LHS ≠ RHS)

• Option - (2) : (5, 81, 4)

⇒\({(5)^3 + (4)^3 \over 2}\) = 81

⇒\({125 + 64 \over 2}\) = 81

⇒\({189 \over 2}\) = 81

⇒94.5 ≠ 81 (LHS ≠ RHS)

• Option - (3) : (7, 40, 3)

⇒\({(7)^3 + (3)^3 \over 2}\) = 40

⇒\({343 + 27 \over 2}\) = 40

⇒\({370 \over 2}\) = 40

⇒185 ≠ 40 (LHS ≠ RHS)

• Option - (4) : (8, 260, 2)

⇒\({(8)^3 + (2)^3 \over 2}\) = 260

⇒\({512 + 8 \over 2}\) = 260

⇒\({520 \over 2}\) = 260

⇒260 = 260 (LHS = RHS)

Hence, "Option - (4)" is the correct answer.

In first dice and second dice:

Given:

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise number are known as opposite numbers in dice.

In first dice and second dice. The symbol 'l' is common.

The left letter will be opposite each other writing them clockwise starting from I.

Hence, the face opposite the H is “@”.

Hence, the correct answer is “@”

• A cube of side 80 cm is painted yellow on all the faces and then cut into smaller cubes of sides 8 cm each.

• The number of smaller cube having all the three faces painted.

All corner cubes are painted on three sides there are 8 corners in cubes.

So, cubes with paint on 3 sides = 8

Hence, "8" is the correct answer.

Additional Information

If a cube has been painted red, blue, and black on pairs of opposite faces and divide it into X parts.

1) Total number of cubes = X³

2) Cubes that have three faces painted = 8 (Because there are only 8 corners in the cube)

3) Cubes which has only two faces painted = (X - 2) × No of Edges (12)

4) Cubes that have only one face painted = (X - 2)² × 6

5) Cubes that have no face painted = (X - 2)³

For this question, the relation is given below -

Logic: If two dice have the same two face values in the given image then the third number is opposite to each other.

In first dice and second dice.

Symbols 'Y' and 'Z' are common.

So, the symbol '&' is the opposite of $.

Hence, the correct answer is “&”

Common number in both the positions = 2

Start with common number 2 moving clockwise.

Opposite letters:

2 ⇒ 6

3 ⇒ 4

1 ⇒ 5

Hence, "1" is the opposite of 5.

A cube of side 18 cm is painted yellow on all the faces and then cut into smaller cubes of sides 3 cm each.

Cube is divided into 18/3 = 6 equal parts, hence n = 6.

Number of cubes with 2 sides painted = 12 (n - 2)

= 12 (6 - 2)

= 12 × 4

= 48 

Hence, '48' is the correct answer. 

A cube of side 12 cm is painted green on all the faces and then cut into smaller cubes of sides 2 cm each.

Cube is divided into 12/2 = 6 equal parts, hence n = 6.

Number of cubes with 1 sides painted = 6(n - 2)²

= 6 (6 - 2)²

= 6 × 4²

= 6 × 16

= 96

Hence, '96' is the correct answer.