1. How many cubes are there which have no face painted? (1) 1 (2) 4 (3) 8 (4) 16

Question

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.

1. How many cubes are there which have no face painted? 

(1) 1 

(2) 4 

(3) 8 

(4) 16 

2. How many cubes have only one face pained? 

(1) 8 

(2) 16 

(3) 24 

(4) 32 

3. How many cubes are there with three faces painted? 

(1) 4 

(2) 8 

(3) 16 

(4) 24 

4. How many cubes are there with two faces painted? 

(1) 24 

(2) 8 

(3) 32 

(4) 12 

5. How many cubes have one face green and one of the adjacent faces black or red? 

(1) 8 

(2) 16 

(3) 24 

(4) 28

Answer 1

1. (3) 8

here n = 4 and n³ = 64 

(n - 2)³  = no face painted, i.e., 8 in number.

2. (3) 24

1 face painted cubes = 6(n - 2)² = 6 x 2² = 24

3. (2) 8

3 face painted cubes = 8 (only corners)

4. (1) 24

2 face painted cubes = 12 (n - 2) = 24

5. (2) 16

1 face green and adjacent face black or red will be on edges i.e., 2 on each edge of 2 faces i.e., 16.