CUBES (C)

EXERCISE - 1

1) Count the number of blocks in the figure.

2) Count the number of cubes
3) The figure is a drawing of piles of blocks. When taken apart, how many blocks would there be?

4) Count the number of blocks

5) Count the number of cubes 

6) Count the number of cubes

7) Count the number of cubes of the following figures:
8) 
9) 
10) 
11) 
12)
13) 
14) 
15)
16) 
18) 
19) 




Answers
1C 2C 3B 4B 5C 6D 7C 8C 9B 10B 11B 12C 13C 14D 15B 16 D 19C 20D 



EXERCISE - 2
1) A cube whose two adjacent faces are coloured is cut in to 64 identical small cubes. How many of these small cubes are not coloured at all ?          

2) A wooden cube is painted Blue on all the four adjourning sides and Green on two opposite sides i.e , top and bottom. It is then cut at equal distances at right angles for time vertically (top to bottom) and two times horizontally (along the sides) as shown in the adjoining figure, where the dotted lines represent the cuts made  Study the diagram and answer the following questions.
1) How many cubes will have one face painted only in Blue ?
A) 1 B) 2 C) 3 D) 4 E) 5                
            
2) How many cubes will have one face painted only in  green.
A) 1 B) 2 C) 3 D) 4 E) 5                                

3) How many cubes are formed in all ?
A) 16 B) 24 C) 27  D) 32 E) 48.                    
        
4) How many cubes will have at least three sides painted ?
A) 12 B) 7 C) 6 D) 3 E) 2                              

5) How many cubes will have no faces pointed at all.
A) 1 B) 2 C) 3 D) 4 E) 5                                


Q.1) A cube, painted yellow on all faces is cut into square 27 small cubes of equal size. How many small cubes are painted on one face only.
A) 1 B) 6 C) 8 D) 12                                      

Q. 2) All surfaces of a cube are coloured. If a number of smaller cubes are taken out from it, each side 1/4 the size of the original cube's side, indicate the number of the cubes with only one side painted.
A) 60 B) 32 C) 24 D) 16                               

Q. 3) Directions: A cube is painted blue on all faces is then cut into 125 cubes up equal size. Answer the following questions on this statement.
 
1) How many cubes are not painted on any face ?
A)  8 B) 16 C) 27 D)  36 E) 54.                    

2) How many cubes are painted on one face only ?
 A) 16 B) 32 C) 48 D) 54 E) 72.                     

Q. 4) A cube of a white material is painted black on all its surfaces. If it is cut into 125 smaller cubes of the same size, then how many cubes will have two sides painted black ?
A) 8 B) 16 C) 22  D) 44  E) none.                

Q. 5) A cube painted yellow on all faces in cut into 27 small cubes are equal sizes. Answer the questions that follow:
1) How many cubes are painted on one face only ?
A) 1 B) 6 C) 8 D) 12.                                     

2) How many cubes are not painted on any face ?
A) 1 B) 4 C) 6 D) 8.                                       


Q. 6. Directions : 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:
 1) How many cubes have no faces coloured ?
A) 24 B) 16 C) 8 D) 0.                                

2) How many cubes are there which have only one pace coloured ?
A) 4 B) 8 C) 16 D) 24.                                   

3) How many cubes have two red opposite faces ?
A) 0B) 8 C) 16 D) 24.                                   
             
4) How many cubes have three faces coloured.
A)  24 B) 16  C) 8  D) 4                               

Q.7. Directions : 125 cubes of the same size are arranged in the form of a cube on a table. Then a column of 5 cubes is removed from each of the four corners. All the exposed faces of the rest of the solid (except the face touching the table) are coloured red. Now, answer these questions based on the above statement:
 
1) How many small cubes are there in the solid after the removal of the columns ? 
A) 120 B) 110 C) 105  D) 100                       

2) How many cubes do not have any coloured face ?
A) 12 B) 24 C) 36  D) 48                              

3)  How many cubes have only one red face each ?
A) 40 B) 25 C) 20  D) 15                              

4) How many cubes have more than two coloured faces each ?
A) 8 B) 20 C) 36 D) 44                               

Q.8. Directions : A solid cube of each side 8 cms has been painted red, blue and black on pairs of opposite faces. It is then cut into cubical blocks of each side 2 cms.

1) How many cubes have no face painted ?
A) 0 B) 4 C) 8 D) 12                                      

2) How many cubes have only one face painted ?
A) 8 B) 16 C) 24  D) 28                                

3) How many cubes have only two faces painted ?
A) 8 B) 16 C) 20  D) 24                                

4) How many cubes have three faces painted ?
A) 0 B) 4 C) 6 D) 8                                        

5) How many cubes have three faces painted with different colours ?
A) 0 B) 4 C) 8  D) 12                                    

6) How many cubes have two faces painted red and black and all other faces unpainted ?
A) 4 B) 8 C) 16 D) 32                                  

7) How many cubes have only one face painted red and all other faces unpainted.
A) 4 B) 8C) 12 D) 16                                    

8) How many cubes have two faces painted black ?
A) 2 B) 4 C) 8 D) none                                 

9) How many cubes have one face painted and one face painted red ? (the other faces is may be painted or unpainted)
A) 32 B) 16 C) 10 D) 8                                 

10) How many cubes are there in all ?
A) 64 B) 48 C) 32  D) 16                            

Q. 9. Directions:  A cube of side 10cm is coloured red with a 2 cm wide green strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size. Answer the following questions based on this statement :

1)  How many cubes have three green faces each?
A) 0 B) 4 C) 8 D) 16                                     

2) How many cubes have one face red and an adjacent face green ?
A) 0 B) 6 C) 8 D) 16                                     

3) How many cubes have least one face coloured?
A) 76 B) 89 C) 98 D) 102                            

4) How many cubes have at least two green faces each?
A) 8 B) 27 C) 44 D) 63                                

5) How many cubes are without any colour ?
A) 64 B) 27  C) 12 D) 0                               

Q. 10. Directions: A cube is painted red on two adjacent faces, yellow on the two faces opposite to the red faces and green on the remaining faces. It is then cut into 64 smaller cubes of equal size. Answer the following questions based on this information :

1) How many cubes are painted on all faces ?
A) 16 B) 8 C) 4 D) 0                                     

2) How many cubes are there which have no face painted?
A) 24 B) 16 C) 8 D) 4                                   

3) How many cubes are painted yellow on one face only ?
A) 4 B) 8 C) 16 D) 32                                  

4) How many cubes have three face painted ?
A) 16 B) 12 C) 8 D) 6                                   

5) How many cubes have one face green and one of the adjacent face red or yellow ?
A) 24 B) 20 C) 16 D)  12                              

6)  How many cubes are painted on two faces only and with the same colour ?
A)  16 B) 8 C) 4 D) 0                                     

Q. 11. Directions : A cube is coloured red on one face, green on the opposite face, yellow on another face and blue on a face adjacent to the yellow face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size.
1) How many cubes are uncoloured on all the faces ?                                          
A) 64  B) 48 C) 36  D) 27                             
2) How many cubes have at least two   coloured faces ?                                       
A) 23 B) 21 C) 19 D) 15                             
3) How many cubes are coloured red on face and have the remaining faces uncoloured?                                        
A) 16 B) 12 C) 20 D) 8                         
4)  How many cubes have atleast one green face ?                                 
A)  5 B) 16 C) 25 D) 32.                          
5) How many cubes are coloured blue on one face, red or green on another face and have four uncoloured faces ?
A) 4 B) 8 C? 12 D) 16                               

Q.12. A cube is painted red on two            adjacent faces and on the 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 one red coloured face only ?                     
A) 24 B) 20 C) 16 D) 12.                               
Q. 13. Directions: A cube is cut into two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining, while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of the same size. The 64 cubes are then mixed up.                                           Based upon the above information, answer the following questions:                
1) How many cubes have no coloured face at all ?                                               
A) 16 B) 8 C) 4 D) 0                                   
                         
2) How many cubes have only one     coloured face?                                              A) 8 B) 16 C) 20 D) 24                                                 
3) How many cubes have two red and one green face?                                        
A) 4 B) 8 C) 12 D) 16                                
                
4) How many cubes have one face red another green?                                        
A) 32 B) 24 C) 16 D) 8                             

5) What is the number of cubes with at least one green face .                               
A) 46 B) 38 C) 36 D) 28                            

Q. 14. Directions: A solid cube has been painted yellow, blue and black and pairs of opposite faces. The cube is then cut into 36 smaller cubes such that 32 cubes are of the same size while four others are of bigger size. Also no face of any of the bigger cubes is painted blue.        
              
1) How many cubes have at least one face painted blue ?                                  
A) 0 B) 8 C) 16 D) 32.                               

2) How many cubes have only one face printed ?                                             
A) 0 B) 4 C) 8 D) 12                                 

3) How many cubes have only two faces painted ?                                                 
A) 24 B) 20 C) 16 D) 8                            
                  
4) How many cubes have two or more faces painted ?                                        
A) 36 B) 34 C) 28 D) 24                           

5) How many cubes have only three faces painted?                                         
A) 8 B) 4 C) 2 D) 0                                   

6) How many cubes do not have any of their faces painted yellow?                      
A) 0 B) 4 C) 8 D) 6                                     

7) How many cubes have atleast one of their faces painted black?                  
A) 0 B) 8 C) 16 D) 20.                                

8) How many cubes have atleast one of their faces painted Yellow or blue ?
A) 36 B) 32 C) 16 D) 0                         

9) How many cubes have no faces     painted?                                                        A) 8 B) 4 C) 1 D) 0                                     

10) How many cubes have two faces painted yellow and black respectively 
A) 0 B) 8 C) 12 D) 16                                

Q. 15. Directions: A cube is coloured Red on two opposite faces, Blue one two adjacent faces and yellow on the two remaining faces. It is then cut into two halves along the plane parallel to the Red faces. One piece is then cut into 4 equal cubes and the other one into 32 equal cubes. Now, answer the following questions based on the above statements :
1) How many cubes do not have any           coloured face ?                                       
A) 0 B) 2 C) 4 D) 8                                       

2) How many cubes do not have any Red face?                                                              
A) 8 B) 16 C) 20 D) 24                              

 3) How many cubes have at least two coloured faces ?                                          
A) 20 B) 24 C) 28 D) 32                              

4) How many cubes have each a Yellow face with other faces blank ?                    
A) 4 B) 14 C) 16 D) 17                                 

5) How many cubes have at least one Blue faces ?                                                
A) 14 B) 15 C) 17 D) 20.                             

Q. 16. Directions: A cube is coloured red on 3 adjacent faces. It is then cut (once horizontally and once vertically) into 4 cuboids of equal size. Each of these cuboids is coloured green on all the uncoloured faces and is then cut (once horizontally and once vertically) into 4 cuboids of equal size.

1) How many cuboids have at 3 red faces each ?                                                 
A) 1 B) 2 C) 4 D) 8                                        

2) How many cuboids have two green faces each ?                                              
A) 3 B) 5 C) 6 D) 9                                      

3) How many cuboids have three green faces each?                                                
A) 4 B) 5 C) 7 D) 9                                      

Q. 17. Directions: Some equal cubes are arranged in the form of a solid block as shown in the figure. All the visible surfaces of the block (except bottom) are then painted.        
                                         
1) How many cubes do not have any of the faces painted ?                                   
A) 27 B) 32 C) 36 D) 40                            

2) How many cubes have only one face painted?                                                    
A) 9 B) 45 C) 57 D) 62                              

3) How many cubes have only two faces painted ?                                                     
A) 0 B) 16 C) 20 D) 24                               

4) How many cubes have only three     faces painted ?                                         
A) 4 B) 12 C) 16 D) 20.                           

Q. 18. Directions: A solid black is formed by arranging some cubes of equal dimensions, as shown in the figure. Whole of the black (visible surfaces) except the base has been coloured pink. Answer the question based upon this information :

1) How many cubes have four faces coloured ?                                                   
A) 0 B) 1 C) 2 D) 3                                      

2) How many cubes have exactly 3 faces coloured ?                                               
A) 2 B) 4 C) 8 D) 11.                                 

3) How many cubes exactly two faces coloured ?                                              
A) 9 B) 11 C) 13 D) 15                           

4) How many cubes have only one face coloured ?                                                    
A) 22 B) 24 C) 25 D) 27                              

5) How many cubes are not coloured on any face ?                                                   
A) 6 B) 8 C) 9 D) 11                                    

Q. 19. Directions: In the figure shown there are 27 cubes numbered from 1 to 27. Answer the following questions:

1) Number of cubes which have                  maximum number of faces touching   the other cubes is                                      
A) 1 B) 2 C) 3 D) 4                                      

2) Number of cubes which have                minimum number of faces touching the other cubes is :                                           
A) 1 B) 2 C) 4 D) 6                                      

3) Which of the cure cubes 3,7, 20 or 27 touches the maximum number of cubes.
A) 3 B) 8 C) 20 D) 25                                  

4) Which of the cubes 6,13, 19 or 25        touches maximum number of cubes?
A) 6 B) 13 C) 19 D) 25                                

5) Which of the cube 7, 21, 22 or 23        touches minimum number of cubes ?
A) 7 B) 21 C) 22 D) 23                                 

6) Which cube is hidden under cube 19 ?
A) 18 B) 20 C) 24 D) 25                               

7) What cube is hidden under 13 ?           
A) 5 B) 14 C) 15 D) 19                                

8) How many cubes are hidden and so  could not be numbered?                             
A) 8 B) 6 C) 5 D) 4.                                 

9) How many cubes have their faces     touching four other cubes ?                      
A) 9 B) 10 C) 12 D) 13                                

10) The cubes having their five faces   touching other cubes are :                         
A) 7, 14, 20 B) 13, 14, 20 C) 13, 18, 22 D) 13, 14 ,18, 20, 22.                                         









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