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.