Question 1

Count the number of cubes in the given figure.

Accepted Answer

In the figure, there are 5 columns containing 4 cubes each; 33 columns containing 3 cubes each; 9 columns containing 2 cubes each and 3 columns containing 1 cube each. ∴ Total Number of cubes = ( 5 x 4) + (33 x 3) + (9 x 2) + (3 x 1) = 20 + 99 + 18 + 3 = 140

Question 2

Find the total number of cubes in the given figure?

Accepted Answer

(Total numbers of cubes in a line x Number of stack / tower) + ... = (6x1)+(5x2)+(4x3)+(3x4)+(5x2)+(6x1) = 6+10+12+12+10+6 = 56

Question 3

A cube is painted blue on two adjacent surfaces and black on the surfaces opposite to blue surfaces and green on the remaining faces .Now the cube is cut into 216 smaller cubes of equal size.

Accepted Answer

We know that Cubes with no surface painted can be find using x - 2 3 , where x is number of cuttings. Here x=6. ∴ 6 - 2 3 = 64

Question 4

Choose the box that is similar to the box formed from the given sheet of paper (A). (A)

Accepted Answer

When the sheet in fig. (A) is folded, then one of the faces of the cube formed will be of the form and this face will lie opposite the face bearing a square. Also, one of the blank faces lies opposite another blank face and the third blank face lies opposite the face bearing an '=' sign. Clearly, all the three blank faces cannot appear adjacent to each other. So, the cube shown in fig. (2) which has all the three blank faces adjacent to each other cannot be formed. Hence, only the cubes shown in figures A, C and D can be formed.

Question 5

Count the number of cubes in the given figure.

Accepted Answer

In the figure, there are 34 columns containing 2 cubes each. ∴ Total number cubes = (34 x 2) = 68

Question 6

Count the number of cubes in the given figure.

Accepted Answer

Clearly, there are 4 columns containing 1 cube each, 4 columns containing 2 cubs each and 1 column containing 3 cubes. Hence, there are (4 x 1) + (4 x 2) + (1 x 3) = 4 + 8 + 3 = 15 cubes in the given figure.

Question 7

Count the number of cubes in the given figure.

Accepted Answer

In the figure, there are 9 columns containing 5 cubes each, 7 columns containing 4 cubes each, 5 columns containing 3 cubes each and 1 column containing 1 cube. ∴ Total number of cubes = (9 x 5) + (7 x 4) + (5 x 3) + (1 x 1) = 89

Question 8

Count the number of cubes in the given figure.

Accepted Answer

In the figure, there are 21 columns containing 2 cubes each and 4 columns containing 1 cube each. ∴ Total number of cubes = (21 x 2) + (4 x 1) = 42 + 4 = 46.

Question 9

Choose the box that is similar to the box formed from the given sheet of paper (A). (A)

Accepted Answer

when a cube is formed by folding the sheet shown in fig. (A), then is one of the faces of the cube and this face lies opposite to a blank face. Also, a face bearing a square lies opposite to another blank face. The remaining two blank faces lie opposite to each other. Clearly, in the cube shown in fig. (1), the face consisting of the four symbols is not the same as that formed (as shown above). Hence, the cube in fig. (1) cannot be formed

Question 10

Two positions of a cube are shown. What number will come on the opposite to face containing '4'?

Accepted Answer

Question 11

Three positions of a cube are shown in the figure. What will come on the face opposite to N?

Accepted Answer

Question 12

Two positions of a cube are shown below. What will come opposite to face containing 'δ'?

Accepted Answer

Question 13

Three positions of a cube are shown below. What will come opposite to face containing '5'

Accepted Answer

Question 14

What will come opposite to face containing 'E' in the cube?

Accepted Answer

Question 15

Choose the box that is similar to the box formed from the given sheet of paper (X).

Accepted Answer

The fig. (X) is similar to the Form VI. So, when a cube is formed by folding the sheet shown in fig. (X), then is one of the faces of the cube. However, the cube in fig. (1) has two such faces and fig. (4) has a face which is completely shaded. So, these two cubes cannot be formed. Hence, only the cubes in figures (2) and (3) can be formed.

Question 16

Choose the box that is similar to the box formed from the given sheet of paper (X).

Accepted Answer

The fig. (X) is similar to the Form I. So, when the sheet shown in fig. (X) is folded to form a cube then one of the two half-shaded faces lies opposite to one of the blank faces and the other half-shaded face lies opposite to another blank face. The two remaining blank faces lie opposite to each other. Thus, both the cubes shown in figures (1).and (4) can be formed when the sheet shown in fig. (X) is folded. Also, though the cubes shown in figures (2) and (3) have faces that can appear adjacent to each other but the cube formed by folding the sheet in fig. (X) cannot be rotated to form either of the two. Hence, the cubes in figures (2) and (3) cannot be formed.

Question 17

How many dots lie opposite to the face having three dots, when the given figure is folded to form a cube?

Accepted Answer

The given figure is similar to Form V. Therefore, when this figure is folded to form a cube then the face bearing six dots will lie opposite the face bearing three dots.

Question 18

Choose the box that is similar to the box formed from the given sheet of paper (X).

Accepted Answer

The fig. (X) is similar to Form II. So, when the sheet shown in fig. (X) is folded to form a cube then the two half-shaded faces lie opposite to each other, the face bearing a circle lies opposite to one of the two blank faces and the two remaining blank faces lie opposite to each other. Therefore, the cubes shown in fig. (4) which has the two half-shaded faces adjacent to each other, cannot be formed by folding the sheet shown in fig. (X). Also, the cube shown in fig. (2) has the face bearing a circle adjacent to two blank faces. This is not possible since there is one blank face opposite to the circle and one blank face opposite to the third blank face. Hence, only the cubes in figures (1) and (3) can be formed.

Question 19

Choose the box that is similar to the box formed from the given sheet of paper (X).

Accepted Answer

The fig. (X) is similar to Form II. So, when a cube is formed by folding the sheet shown in fig. (X), then the two half-shaded faces lie opposite to each other and one. of the three blank faces appears opposite to the face bearing a dot. Clearly, each one of the four cubes shown in figures (1), (2), (3) and (4) can be formed by folding the sheet shown in fig. (X).

Question 20

Choose the box that is similar to the box formed from the given sheet of paper (X).

Accepted Answer

When the sheet in fig. (X) is folded, then one of the faces of the cube formed will be of the form and this face will lie opposite the face bearing a square. Also, one of the blank faces lies opposite another blank face and the third blank face lies opposite the face bearing an '=' sign. Clearly, all the three blank faces cannot appear adjacent to each other. So, the cube shown in fig. (2) which has all the three blank faces adjacent to each other cannot be formed. Hence, only the cubes shown in figures A, C and D can be formed.

Cubes and Dice Questions