### Cube and Dice Test

1. Directions (Qs. 1 – 4) : A cube is coloured red on all faces. It is cut into 64 smaller cubes of equal size. Now, answer the following questions based on this statement :How many cubes have no face coloured?

2. Directions (Qs. 1 – 4) : A cube is coloured red on all faces. It is cut into 64 smaller cubes of equal size. Now, answer the following questions based on this statement :How many cubes are there which have only one face coloured?

3. Directions (Qs. 1 – 4) : A cube is coloured red on all faces. It is cut into 64 smaller cubes of equal size. Now, answer the following questions based on this statement :How many cubes have two red opposite faces?

4. Directions (Qs. 1 – 4) : A cube is coloured red on all faces. It is cut into 64 smaller cubes of equal size. Now, answer the following questions based on this statement :How many cubes have three faces coloured?

5. Directions (Qs. 5-9) : A wooden cube is painted Blue on all the four adjoining sides and Green on two opposite sides i.e. top and bottom. It is then cut at equal distances at right angles four times vertically (top to bottom) and two times horizontally (along the sides) as shown in the figure where the dotted lines represents the cuts made. Study the diagram and answer the following questions : How many cubes will have one face painted only in Blue?

6. Directions (Qs. 5-9) : A wooden cube is painted Blue on all the four adjoining sides and Green on two opposite sides i.e. top and bottom. It is then cut at equal distances at right angles four times vertically (top to bottom) and two times horizontally (along the sides) as shown in the figure where the dotted lines represents the cuts made. Study the diagram and answer the following questions : How many cubes will have one face painted only in Green?

7. Directions (Qs. 5-9) : A wooden cube is painted Blue on all the four adjoining sides and Green on two opposite sides i.e. top and bottom. It is then cut at equal distances at right angles four times vertically (top to bottom) and two times horizontally (along the sides) as shown in the figure where the dotted lines represents the cuts made. Study the diagram and answer the following questions : How many cubes are formed in all?

8. Directions (Qs. 5-9) : A wooden cube is painted Blue on all the four adjoining sides and Green on two opposite sides i.e. top and bottom. It is then cut at equal distances at right angles four times vertically (top to bottom) and two times horizontally (along the sides) as shown in the figure where the dotted lines represents the cuts made. Study the diagram and answer the following questions : How many cubes will have at least three sides painted?

9. Directions (Qs. 5-9) : A wooden cube is painted Blue on all the four adjoining sides and Green on two opposite sides i.e. top and bottom. It is then cut at equal distances at right angles four times vertically (top to bottom) and two times horizontally (along the sides) as shown in the figure where the dotted lines represents the cuts made. Study the diagram and answer the following questions : How many cubes will have no face painted at all?

10. Directions (Qs. 10-12) : Three adjacent faces of a cube are coloured blue. The cube is then cut (once horizontally and once vertically) to form four cuboids of equal size, each of these cuboids is coloured pink on all the un-coloured faces and is then cut (as before) into four cuboids of equal size.How many cuboids have two faces coloured pink?

11. Directions (Qs. 10-12) : Three adjacent faces of a cube are coloured blue. The cube is then cut (once horizontally and once vertically) to form four cuboids of equal size, each of these cuboids is coloured pink on all the uncoloured faces and is then cut (as before) into four cuboids of equal size.How many cuboids have three faces coloured pink?

12. Directions (Qs. 10-12) : Three adjacent faces of a cube are coloured blue. The cube is then cut (once horizontally and once vertically) to form four cuboids of equal size, each of these cuboids is coloured pink on all the uncoloured faces and is then cut (as before) into four cuboids of equal size.How many cuboids have three faces coloured blue?

13. Directions (Qs. 13-17) : A cube painted red on two adjacent faces and black on the faces opposite to the red faces and green on the remaining faces, is cut into sixty-four smaller cubes of equal size.How many cubes are there which have no face painted?

14. Directions (Qs. 13-17) : A cube painted red on two adjacent faces and black on the faces opposite to the red faces and green on the remaining faces, is cut into sixty-four smaller cubes of equal size.How many cubes have only one face painted?

15. Directions (Qs. 13-17) : A cube painted red on two adjacent faces and black on the faces opposite to the red faces and green on the remaining faces, is cut into sixty-four smaller cubes of equal size.How many cubes have less than three faces painted?

16. Directions (Qs. 13-17) : A cube painted red on two adjacent faces and black on the faces opposite to the red faces and green on the remaining faces, is cut into sixty-four smaller cubes of equal size.How many cubes are there with three faces painted?

17. Directions (Qs. 13-17) : A cube painted red on two adjacent faces and black on the faces opposite to the red faces and green on the remaining faces, is cut into sixty-four smaller cubes of equal size.How many cubes have one face green and one of the adjacent faces black or red?

18. A cube is painted red on two adjacent faces and on one opposite face, yellow on two opposite faces and green on the remaining face. It is then cut into 64 equal cubes. How many cubes have only one red coloured face?

19. From a 10 × 10 × 10 cube, which is formed by combinations of 1 × 1 × 1 cubes, a layer of the smaller cubes is removed. What will be the number of 1 × 1 × 1 cubes present in this new cube?

20. A 5 × 5 × 5 cube is formed by using 1 × 1 × 1 cubes. If we add another layer of such 1 × 1 × 1 cube in the 5 × 5 × 5 cube. What will be the number of 1 × 1 × 1 cubes in the newly formed cube?