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The following questions are based on the information given below:
  1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
  2. The opposite faces of dimensions 4 x 3 are coloured yellow.
  3. The opposite faces of other dimensions 4 x 3 are coloured red.
  4. The opposite faces of dimensions 3 x 3 are coloured green.
  5. Now the cuboid is cut into small cubes of side 1 cm.
Question -
How many small cubes have three faces coloured ?
  • a)
    24
  • b)
    20
  • c)
    16
  • d)
    8
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Directions to Solve ...
Such cubes are related to the corners of the cuboid and there are 8 corners.
Hence, the required number is 8.
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Directions to Solve ...
Understanding the Cuboid Dimensions
The cuboid has the dimensions of 4 cm x 3 cm x 3 cm. It is made up of small cubes of 1 cm each, resulting in a total of 4 x 3 x 3 = 36 small cubes.
Coloring of the Faces
- Yellow Faces: The two opposite faces measuring 4 cm x 3 cm.
- Red Faces: The other two opposite faces of dimensions 4 cm x 3 cm.
- Green Faces: The two opposite faces measuring 3 cm x 3 cm.
Identifying the Small Cubes with Three Colored Faces
To determine how many small cubes have three faces colored, we need to identify the corners of the cuboid:
- A cuboid has 8 corners.
- Each corner cube will have three faces exposed and thus colored.
Calculating the Corner Cubes
- The corner cubes are located at the intersections of the colored faces.
- Since each corner is shared by three different colored faces, each corner cube will have three faces colored.
Conclusion
Thus, there are a total of 8 small cubes with three faces colored.
The correct answer is option D: 8.
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