Question

A cube is painted red on two adjacent surfaces and black on the surfaces opposite to red surfaces and green on the remaining faces. now the cube is cut into 64 smaller cubes of equal size. a) how many smaller cubes have only one surface painted? b) how many smaller cubes will have no surface painted?

Answer 1

24 smaller cubes have only one surface painted. 8 smaller cubes will have no surface painted

• Cube is divided into 64 equal cubes
• so it should be cut into 4 equal parts on each side
• (4³ = 64)
• We know,
• red on two adjacent surfaces and black on the surfaces opposite to red surfaces and green on the remaining faces
• The cubes at the edges and corners will have more than one surface painted.
• They are 32 in number
• All the cubes at the surface will have at least one side painted = 56
• Cubes with only one surface painted = 56 - 32 = 24
• Cubes that cannot be seen from outside are not painted even at one side = 64 -56 = 8
• #SPJ3