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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 will have only one face coloured ?
  • a)
    10
  • b)
    12
  • c)
    14
  • d)
    18
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Directions to Solve ...
Number of small cubes having only one face coloured = 2 x 2 + 2 x 2 + 2 x 1
= 4 + 4 + 2
= 10
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Directions to Solve ...
Given Information:
- Dimensions of the cuboid: 4 x 3 x 3 cm
- Opposite faces of dimensions 4 x 3 are coloured yellow
- Opposite faces of other dimensions 4 x 3 are coloured red
- Opposite faces of dimensions 3 x 3 are coloured green
- Cuboid is cut into small cubes of side 1 cm

To find: How many small cubes will have only one face coloured?

Solution:
To solve this problem, we need to count the number of small cubes that have only one face coloured. Let's consider each colour separately.

Yellow Colour:
- The dimensions of the yellow coloured faces are 4 x 3.
- When we cut the cuboid into small cubes of 1 cm, the length of the yellow face becomes 3 cm and the breadth becomes 4 cm.
- So, the number of small cubes that have only one yellow face is (3 x 4) = 12.

Red Colour:
- The dimensions of the red coloured faces are also 4 x 3.
- When we cut the cuboid into small cubes of 1 cm, the length of the red face becomes 3 cm and the breadth becomes 4 cm.
- So, the number of small cubes that have only one red face is (3 x 4) = 12.

Green Colour:
- The dimensions of the green coloured faces are 3 x 3.
- When we cut the cuboid into small cubes of 1 cm, the length and breadth of the green face become 3 cm each.
- So, the number of small cubes that have only one green face is (3 x 3) = 9.

Therefore, the total number of small cubes that have only one face coloured is:
= Number of small cubes with one yellow face + Number of small cubes with one red face + Number of small cubes with one green face
= 12 + 12 + 9 = 33

Hence, the correct option is (A) 10.
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Directions to Solve The following questions are based on the information given below:There is a cuboid whose dimensions are 4 x 3 x 3 cm.The opposite faces of dimensions 4 x 3 are coloured yellow.The opposite faces of other dimensions 4 x 3 are coloured red.The opposite faces of dimensions 3 x 3 are coloured green.Now the cuboid is cut into small cubes of side 1 cm. Question - How many small cubes will have only one face coloured ?a)10b)12c)14d)18Correct answer is option 'A'. Can you explain this answer?
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