Question 1

A solid cube of 4 inches has been painted Red, Green and Black on pair of opposite faces. It has then been cut into one inch cubes. How many cubes have only four faces painted?

Accepted Answer

On the basis of the given all information in above question , we can say that A solid cube of 4 inches has been painted Red, Green and Black on pair of opposite faces. No cube will have four faces painted.

Question 2

A solid cube of 4 inches has been painted red, green and black on pair of opposite faces. It has been cut into one inch cubes. How many cubes have only two faces painted?

Accepted Answer

As per the given all information in above question , we can say that There are 8 cubes in Layer 1, 4 cubes in Layer 2, 4 cubes in Layer 3, and 8 cubes in Layer 4 which have only two faces painted. Thus, there are 8 + 4 + 4 + 8 = 24 such cubes.

Question 3

How many cubes are there in this diagram?

Accepted Answer

On the basis of above given figure , we can see that Count the numbers of cubes in given figure = 12 Hence , There are 12 cubes.

Question 4

How many cubes are unseen in the figure?

Accepted Answer

From the given above figure , we can count the total numbers of cubes :- Altogether there are 9 + 5 +1 = 15 cubes. 10 cubes are seen in the figure. So, five cubes are unseen in the figure.

Question 5

Which of the following cubes can be created by folding the given figure?

Accepted Answer

As per the given above open dice , we have When folded in the form of a cube, then 'F' appears opposite 'B'; 'E' appears opposite 'C' and 'A' appears opposite 'D'. In option (1) 'F' is adjacent to 'B'. In option (3) 'E' is adjacent to 'C'. In option (4) 'D' is adjacent to 'A'.

Question 6

Study the 3 different positions of a cube given below and answer what number comes opposite to 2?

Accepted Answer

On the basis of following pattern in given dices , we can say that The numbers 2, 4, 5 and 6 are on the adjacent faces of number 3. So, number 1 lies opposite 3. The number 5 is on the adjacent faces of numbers 4 and 6. So, number 5 lies opposite 2.

Question 7

The sides of a cube show the colours of rainbow. Two positions of the cube are shown below. Which of the colours of rainbow is left out?

Accepted Answer

As per the given pattern in question figure , we can find the similar next position of given dice . The seven colours of a Rainbow are: Violet, Indigo, Blue, Green, Yellow, Orange and Red. Thus, Violet colour of rainbow is left out.

Question 8

Choose the cube that will be formed by folding the sheet of paper shown in the problem figure.

Accepted Answer

We follow the given pattern :- After folding the sheet of paper in the form of a cube: Ο will lie opposite Δ □ will lie opposite ♥ ◊ will lie opposite ♣ Symbols □ and ♥ cannot be on adjacent faces. So, Answer Figure (3) can be ruled out. Symbols ◊ and ♣ cannot be on adjacent faces. So, Answer Figure (4) can be ruled out. Ο and Δ can not be on adjacent sides. Hence options (1) is not true. Hence option (2) is true.

Question 9

The solid so formed by joining unit cubes is rotated to obtain different positions, which of these cannot be the shape after it has turned?

Accepted Answer

As per the given pattern in question figure , we can find the similar next position of given dice . The shape given in the option (3) is not appropriate.

Question 10

Which symbol will appear on the face opposite to the face of a circle O in the cube given below?

Accepted Answer

We follow the given pattern :- Symbols Δ, ◊, □ and ▲ lie on the faces adjacent to the symbol *Omicron;. Therefore,◎ lies opposite Ο.

Question 11

How many cubes are there in the diagram?

Accepted Answer

From the above given diagram , we can say that Six cubes are visible and four cubes are hidden. Thus , there are 10 cubes .

Question 12

Six faces of the cube are painted with different colors as shown below. In figure 3, which color is opposite to RED?

Accepted Answer

We follow the given pattern :- Orange, Yellow, Red and Black colours are on the faces adjacent to Pink colour. Therefore, Blue colour is opposite to Pink colour. Pink, Black, Blue and Yellow colours on the faces adjacent to Red colour. Therefore, Orange colour is opposite to Red colour.

Question 13

In the given cube, which color is opposite to Blue?

Accepted Answer

As per the given pattern in question figure , we can find the similar next position of given dice . Yellow, Green, Blue and Violet are on the faces adjacent to Red colour. Therefore, sixth colour is opposite to Red. From the four views of cube, it is clear that yellow is opposite to Blue.

Question 14

How many cubes are there in below figure?

Accepted Answer

There are total 42 cubes present in the upper portion. Then total cubes be 42 × 2 = 84 Second method to find out the number of cubes/blocks. 24 columns with 2 cubes each = 24 × 2 = 48 14 columns with 2 cubes each = 28 4 columns with 2 cubes each = 8 Total cubes = 48 + 28 + 8 = 84

Question 15

How many cubes/blocks are there in below figure?

Accepted Answer

There are 20 cubes.

Question 16

How many cubes/blocks are there in below figure?

Accepted Answer

15 × 3 + 13 × 2 + 11 × 1 = 82 cubes

Question 17

Two positions of a block are shown below (i) and (ii). When 2 is at the bottom which number will be at the top?

Accepted Answer

Number three is common in both the figures we assume the block in figure (ii) to be rotated so that three appears at the same position as in figure (i) and the numbers 5 and 2 move to the faces hidden behind the numbers 4 and 6 respectively. Thus the combined figure will have 3 on right hand side face, 4 on the front face, 6 on the top face, 5 on the rear face and 2 on the bottom face. Clearly when 2 is at the bottom, then 6 is at the top.

Question 18

Two positions of a dice are shown below (i) and (ii). When 3 is at the top which number will be at the bottom?

Accepted Answer

as number 6 position is same in both the figures. We can assume that the dice to be rotated so that 6 remains on the same face and 1,3,4 and 5 will be arranged ascending order as all are adjacent to 6. Hence, when 3 is in top, 5 will be at bottam.

Question 19

A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing 2.

Accepted Answer

from figure i, ii and iv we conclude that 6, 4, 3 and 1 lie adjacent to 2. Hence 5 be opposite of 2. For the better understanding take a dice ans apply the same steps which is mentioned above.

Question 20

Among the four alternatives choose which one can be the similar box as the question figure.

Accepted Answer

option (a) and option (d) will be eliminated as we see the figure as the pattern face is adjacent to face C, which cannot be possible. In Option (b) D and E both are adjacent to C, but there direction should be clock wise. Face D on the left side and face E on the right side that can be possible only when pattern face be on the top.

Cubes and Dice Questions