question_answer

DIRECTIONS (Q. 21-23): A wooden cube is painted blue on all the four adjoining sides and green on two opposite sides i.e. top and bottom. It is then cut at equal distances at right angles four times vertically (top to bottom) and two times horizontally (along the sides) as shown in the figure, where the dotted lines represent the cuts made. Study the diagram and answer the following questions:    

How many cubes are formed in all?

A) 16                               

B) 24

C) 27                   

D) 32

Correct Answer: C

Solution :

    There are 9 cubes in each of the three layers. Thus there are 27 cubes in all.  The figure may be analyzed by dividing it into three horizontal layers: In the top layer, the central cube has only one face painted green, the four cubes at the comer have three face painted one face green and two faces blue. The remaining four cubes have two faces painted one green and one blue. In the middle layer, the central cube has no face painted, four cubes at the comers have two faces painted blue and the reaming four cubes have one face painted blue. In the bottom layer, the central cube has one face painted green and four cubes at the comers have three faces painted two blue and one green. The remaining four cubes have two face painted-one blue and one green.