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

The opposite faces of the cube are shown below:

On folding the cube, the following faces are opposite to each other:

 is opposite to 

 is opposite to 

 is opposite to  

As we know that, no two opposite surfaces are adjacent to each other.

Option 1:  and  are adjacent  to each other

∴ The cube in option 1 cannot be made on the given unfolded cube in the question figure, as two opposite sides are adjacent to each other.

Option 2: No opposite surfaces are adjacent to each other.

∴ The cube in option 2 can be made on the given unfolded cube in the question figure.

Option 3: No opposite surfaces are adjacent to each other.

∴ The cube in option 3 can be made on the given unfolded cube in the question figure.

Option 4: No opposite surfaces are adjacent to each other.

∴ The cube in option 4 can be made on the given unfolded cube in the question figure.

Hence, the correct answer is "option 1".

The opposite surface of the open dice/cube can be found by the below methods:-

1. Alternate surfaces are opposite to each other.

2. No two opposite surfaces are touched by side or by corners.

Concept :

When two positions of dice is given and no face is common between them then the face which is at the same position of both the dices becomes the opposite pair.

The given positions of the dice:

No number is common in both of the dice.

Thus, It is clear that 1 would be opposite to 2

3 would be opposite to 6

5 would be opposite 4.

Hence, "1 is opposite 2" as per the given positions of the dice.

The opposite faces of the cube are,

As Two opposite faces are never seen together or adjacent to each other:

In Option Figure 1 :- Dark circle and cross are opposite faces but here they are seen together which is wrong.

In Option Figure 2 :- Dark circle and cross are opposite faces but here they are seen together which is wrong.

In Option Figures 4 none of the opposite faces are seen together nor they are adjacent to each other.

Thus option figure 4 can be formed by folding the dice.

∴ The correct representation is 

Hence, the correct answer is option 4).

For find the opposite surface of '51', we need to compare the common surface in the given dices,

Now, number '51' is given in Dice 3 and Dice 4, 

So, From Dice 3 and Dice 4,

When we move in clockwise direction starting from m we get;

→ 51 is the common surface and 52, 53, 54, 56 is the adjacent surface.

So, the remaining '55' will be the opposite face of '51'.

Hence, the correct answer is "Option 2".

The logic followed here is:-

From the given two different cubes the adjacent sides are as shown below :

As 9 is common on both the dice, it is clear that 5, 3, 4, and 2 are adjacent to it, and the remaining i.e., 8 will be opposite to it.

Opposite pairs:

3 → 4

5 → 2

9 → 8

So, the opposite side of "3" will be side "4".

Hence, the correct answer is "4".

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)

⇒$\frac{(3{)}^3+(1{)}^3}{2}$ = 14

⇒$\frac{27+1}{2}$ = 14

⇒$\frac{28}{2}$ = 14

⇒14 = 14 (LHS = RHS)

• (4, 36, 2)​

⇒$\frac{(4{)}^3+(2{)}^3}{2}$ = 36

⇒$\frac{64+8}{2}$ = 36

⇒$\frac{72}{2}$ = 36

⇒36 = 36 (LHS = RHS)

So,

• Option - (1) : (8, 12, 2)​

⇒$\frac{(8{)}^3+(2{)}^3}{2}$ = 12

⇒$\frac{512+8}{2}$ = 12

⇒$\frac{520}{2}$ = 12

⇒260 ≠ 12 (LHS ≠ RHS)

• Option - (2) : (5, 81, 4)

⇒$\frac{(5{)}^3+(4{)}^3}{2}$ = 81

⇒$\frac{125+64}{2}$ = 81

⇒$\frac{189}{2}$ = 81

⇒94.5 ≠ 81 (LHS ≠ RHS)

• Option - (3) : (7, 40, 3)

⇒$\frac{(7{)}^3+(3{)}^3}{2}$ = 40

⇒$\frac{343+27}{2}$ = 40

⇒$\frac{370}{2}$ = 40

⇒185 ≠ 40 (LHS ≠ RHS)

• Option - (4) : (8, 260, 2)

⇒$\frac{(8{)}^3+(2{)}^3}{2}$ = 260

⇒$\frac{512+8}{2}$ = 260

⇒$\frac{520}{2}$ = 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.