Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
In which of these cases can a cube and a cuboid be joined together to form a cuboid?
Last updated May 30, 2026
Correct Answer:
Option D —
A cube of side length 5 cm and a cuboid of dimensions 4 cm × 5 cm × 6 cm
To join a cube and a cuboid together to form one larger, seamless cuboid, the faces that touch each other must match perfectly in size.
A cube has the same length, width, and height. This means every single face of the cube is a perfect square with sides equal to its given length.
For a cuboid to attach seamlessly to one of these square faces, at least one of the faces on the cuboid must match those exact same square dimensions. In other words, two of the cuboid's dimensions must be exactly equal to the side length of the cube.
Evaluating the Options
Case A: The cube has sides of 6 cm by 6 cm. The cuboid's dimensions are 4 cm by 5 cm by 6 cm. The cuboid does not have two dimensions that are 6 cm, so it cannot form a perfect match.
Case B: The cube has sides of 6 cm by 6 cm. The cuboid's dimensions are 4 cm by 5 cm by 5 cm. None of the cuboid's measurements match the 6 cm requirement.
Case C: The cube has sides of 5 cm by 5 cm, meaning its faces are 5 cm by 5 cm squares. The cuboid has dimensions of 4 cm by 5 cm by 5 cm. This cuboid has a face that is exactly 5 cm by 5 cm. If you press these two matching faces together, they will align perfectly and extend the length to form a single new cuboid.
Case D: The cube has sides of 5 cm by 5 cm. The cuboid's dimensions are 4 cm by 5 cm by 6 cm. The cuboid only has one dimension that is 5 cm, so it does not have a matching square face.
Conclusion
The only pair that can attach seamlessly is the one where the cuboid shares two dimensions with the cube.
The correct option is (C).
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
