Question

A cube is painted red on two adjacent faces and on one opposite sides 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.
16
B.
18
C.
12
D.
20

Accepted Answer

C. A $4 	imes 4 	imes 4$ cube has 64 smaller cubes ($n = 4$). Central face cubes (having 1 face painted) per face $= (n-2)^2 = (4-2)^2 = 4$. There are 3 faces painted RED. Number of cubes with only one RED face $= 3 	imes 4 = 12$.

Painted Cube Cut into Smaller Cubes

Explanation

Practise this under exam conditions