Question

A cuboid is divided into 192 identical cubelets. This is done by making minimum number of cuts possible. All cuts are parallel to some of the faces. But before doing so, the cube is painted with green colour on one set of opposite faces. Blue on the other set of opposite faces and red on remaining their pair of opposite faces.
What is the maximum number of cubelets possible which one colored with green colored only?

• A. 48
• B. 64
• C. 96
• D. 72

Answer 1

The correct option is A 48

As we want maximize number of cubelets with green in color only cuboid has to painted with green color on set of opposite faces of 6$\times$8. Hence no of green colored only cubelets will (6 - 2 ) $\times$ (8 - 2) = 4$\times$6 =24 from face. There are two such faces hence maximum total no. of only green painted cubess will be = 24 $\times$2 = 48
Hence option (a)