A cuboid of dimensions 7 cm × 5 cm × 3 cm is painted red, green and blue colour on each pair of opposite…
A cuboid of dimensions 7 cm × 5 cm × 3 cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7 cm × 5 cm, 5 cm × 3 cm, 7 cm × 3 cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1 cm. Which of the following statements is/are correct?
1. There are exactly 15 small cubes with no paint on any face.
2. There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green.
Select the correct answer using the code given below:
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Solution
The cuboid is 7 by 5 by 3, giving 105 unit cubes. Cubes with no paint form the inner block of size $(7-2) \times (5-2) \times (3-2) = 5 \times 3 \times 1 = 15$. So statement 1 is correct. Statement 2 about exactly 6 cubes with one blue and one green face does not hold for the given colour arrangement. Only statement 1 is correct.