If a cube is painted yellow on all faces and cut into 27 small cubes of equal size, then which of the following are correct? I. Six cubes are painted on one face only. II. There is only one cube…
Question and options
If a cube is painted yellow on all faces and cut into 27 small cubes of equal size, then which of the following are correct?
I. Six cubes are painted on one face only.
II. There is only one cube which is not painted on any face.
III. There are six cubes which have two faces painted.
IV. There are eight cubes which have three faces painted.
I. Six cubes are painted on one face only.
II. There is only one cube which is not painted on any face.
III. There are six cubes which have two faces painted.
IV. There are eight cubes which have three faces painted.
- I and II only
- I, II and III only
- I, II and IV only
- III and IV only
Answer and explanation
Correct answer: C - I, II and IV only
In a 3x3x3 cube: 8 corner cubes have 3 faces painted, 12 edge cubes have 2, 6 face-centre cubes have 1, and 1 inner cube has none. So I, II and IV are true; III is false because 12 cubes, not 6, have two faces painted.
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