Question

The surface area of a cube of 4 × 4 × 4 dimensions is painted. The cube is cut into 64 equal cubes. How many cubes have 

(a) 1 face painted? 

(b) 2 faces painted? 

(c) 3 faces painted? 

(d) no face painted? 

Answer 1

If the 4 × 4 × 4 cube is divided into 64 equal cubes then the length of its each side = 1 unit.

[∵ (4×4×4)/64 = 1]

a) No. of cubes (a = 4) have painted 1 face 

= 6(a – 2)² 

= 6(4 – 2)² 

= 6 × 4 = 24

b) No. of cubes have painted 2 faces 

= 12(a – 2) 

= 12(4 – 2) = 24

c) No. of cubes have painted 3 faces 

= 4 × a 

= 4 × 2 = 8

d) No. of cubes have painted no faces 

= (a – 2)³ 

= (4 – 2)³ 

= (2)³ = 8