question_answer

DIRECTIONS: A cube painted red on two adjacent faces and block on the faces opposite to the red faces and green on the remaining faces is cut into sixty-four smaller cubes of equal size. How many cubes are there which have no face painted?

A) 0                    

B) 4

C) 8                    

D) 16

Correct Answer: C

Solution :

Here, Faces ABCD, BCFG are painted with red. Faces ADEH, EFGH are painted with red. Faces CDEF, ABGH are painted with green. No. of divisions on the faces of cubes = 4 Now, the figure may be analyzed by dividing it into four horizontal layers:                    In Layer I: Four central cubes only one face painted green, four cubes at the comers have three faces painted red, green and black. Out of the remaining 8 cubes, four cubes have two faces painted red and green and four cubes have two faces painted black and green. In layer II and III: Four central cubes have no faces painted, four cubes at the comers have two face painted red and black. Out of the remaining 8 cubes four cubes have only one face painted black and four cubes have only one face painted red. In layer IV: Four central cubes have only one face painted green, four cubes at the comers have three faces painted red, green and black. Out of the remaining 8 cubes four cubes have two faces painted green and black and four cubes have two faces painted red and green. There are 8 cubes having no face painted.