Challenge Prelims V1.0 – Day 63 – CSAT Paper

1. A cuboid of dimensions 7cm × 5cm × 3cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7cm × 5cm, 5cm × 3cm, 7cm × 3cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1 cm. Which of the following 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 other painted with green

Select the correct answer using the codes given below: (UPSC 2023)

2. A cube of 3 cm side is divided into smaller cubes of 1 cm. What is the minimum number of cuts required to obtain those smaller cubes?

3. A large cube is made up of 27 small identical cubes. The outside of the larger cube is painted red. How many small cubes will have none of their sides painted?

4. A cube is painted red on two adjacent faces, black on the faces opposite to the red faces and green on the remaining faces. Then the cube cut into 27 smaller cubes of equal size. How many small cubes have both green and red on its face?

5. How many cubes having sides equal to 20cm can be put in a cubical box having each edge equal to 1m?