8th Class
Mathematics
Related to Competitive Exam
Question Bank
Cube and Dice
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 have only one face painted -
A)8
B)16
C)24
D)32
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. Cubes only one face painted or \[{{(n-2)}^{2}}\times 6=24\]