Question-1 If the outer border of width 1 cm of a cube with side 5 cm is painted green on each side and remaining space enclosed by this 1 cm path is painted black. This cube then gets cut into 125 smaller cubes of each side 1 cm. If the smaller cube so obtained is separated, then how many such smaller cubes shall have one face coloured green and the adjacent face coloured black ?
a)16
b)2
c)0
d)8
e)1
Explanation
SOLUTION[ C ]-0
Question-2
The six faces of a wooden cube of side 6 cm are labelled A, B, C, D, E and F respectively. Three of these faces A, B, and C are each adjacent to the other two, and are painted red. The other three faces are not painted. Then, the wooden cube is neatly cut into 216 little cubes of equal size. How many of the little cubes have no sides painted at all?
a)96
b)125
c)108
d)222
e)16
Explanation
SOLUTION[B]-125
Since A, B and C are adjacent faces. If we remove them, the resultant solid will also be a cube with side 5.
Hence total number of cubes unpainted = 53 = 125
