read the passage and answer.
there is a cube in which one pair of opposite faces is painted red, another pair of opposite sides is painted blue and third pair of opposite sides is painted pink.
this cube is now cut into 216 smaller but identical cubes
1. how many small cubes will be there with no red paint at all?
a)121 b)144 c)169 d)100
2.how many small cubes will be there with at least two different colours on thier faces?
a)49 b)64 c)56 d)81
3. how many small cubes will be there without any face painted?
a)64 b)49 c)36 d)25
1. Since each face has 36 cubes, the no. of cubes having red panit = 72
therefore the no of small cubes with no red paint = 216 - 72 = 144
the answer is b)
2. these cubes are all those on the edges of the cube.
the no of cubes with atleast 2 colours of paint = 56 answer is c)
3. th no. of cubes with paint are the no of cubes on csa of the cube ,= 2(6*6) + 2(4*6) + 2(4*4) = 72 + 48 + 32 = 152
thus the no. of cubes without paint = 216 -152 = 64 the answer is a)
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