Cube and Cuboid
✏️ Practice with curated questions covering all difficulty levels. Detailed solutions and expert tips help you master each question type.
Sample Questions
Study MaterialSample Questions – Cube and Cuboid
Cube and Cuboid questions test visualization ability, spatial reasoning, analytical thinking, observation skills, and logical interpretation. These questions are highly important in Banking, SSC, Railway, Insurance, Defence, MBA entrance, and government competitive examinations.
Below are important exam-oriented sample questions with detailed explanations.
Sample Question 1 – Total Smaller Cubes
A cube is divided into 4 equal parts along each edge. How many smaller cubes are formed?
A. 16
B. 32
C. 64
D. 128
Correct Answer: C. 64
Explanation:
Formula:
n³
Here:
n = 4
4³ = 64
Sample Question 2 – Minimum Number of Cuts
What is the minimum number of cuts required to divide a cube into 5 × 5 × 5 smaller cubes?
A. 9
B. 10
C. 12
D. 15
Correct Answer: C. 12
Explanation:
Formula:
3(n − 1)
3(5 − 1) = 12
Sample Question 3 – Cubes with Three Faces Painted
A large cube is painted on all outer surfaces and divided into smaller cubes. How many cubes will have exactly three faces painted?
A. 4
B. 6
C. 8
D. 12
Correct Answer: C. 8
Explanation:
Corner cubes always have three faces painted.
Every cube has:
8 corners
Sample Question 4 – Cubes with Two Faces Painted
A cube is divided into 6 equal parts along each edge. How many smaller cubes have exactly two faces painted?
A. 24
B. 36
C. 48
D. 60
Correct Answer: C. 48
Explanation:
Formula:
12(n − 2)
12(6 − 2) = 48
Sample Question 5 – Cubes with One Face Painted
A cube is divided into 5 equal parts along each edge. How many smaller cubes have exactly one face painted?
A. 24
B. 36
C. 54
D. 64
Correct Answer: C. 54
Explanation:
Formula:
6(n − 2)²
6(5 − 2)²
= 6 × 9
= 54
Sample Question 6 – Cubes with No Face Painted
A cube is divided into 7 equal parts along each edge. How many smaller cubes remain unpainted?
A. 64
B. 100
C. 125
D. 216
Correct Answer: C. 125
Explanation:
Formula:
(n − 2)³
(7 − 2)³ = 5³ = 125
Sample Question 7 – Visible Cubes
A cube is divided into 4 equal parts along each edge. How many cubes are visible from outside?
A. 48
B. 56
C. 64
D. 72
Correct Answer: B. 56
Explanation:
Formula:
n³ − (n − 2)³
4³ − 2³
64 − 8 = 56
Sample Question 8 – Cube Folding
In a folded cube, which faces can never touch each other?
A. Adjacent faces
B. Side faces
C. Opposite faces
D. Corner faces
Correct Answer: C. Opposite faces
Explanation:
Opposite faces never share a common edge.
Sample Question 9 – Cube Rotation
What changes after cube rotation?
A. Opposite faces
B. Adjacent faces
C. Face orientation
D. Number of edges
Correct Answer: C. Face orientation
Explanation:
Rotation changes visible orientation but not face relationships.
Sample Question 10 – Total Edge Cubes
A cube is divided into 8 equal parts along each edge. Find the number of edge cubes excluding corners.
A. 48
B. 60
C. 72
D. 96
Correct Answer: C. 72
Explanation:
Formula:
12(n − 2)
12(8 − 2)
= 12 × 6
= 72
Sample Question 11 – Interior Cubes
A cube is divided into 10 equal parts along each edge. How many cubes are completely hidden inside?
A. 216
B. 512
C. 729
D. 1000
Correct Answer: B. 512
Explanation:
Formula:
(n − 2)³
(10 − 2)³
= 8³
= 512
Sample Question 12 – Face Cubes
A cube is divided into 6 equal parts along each edge. Find the number of cubes having exactly one face painted.
A. 54
B. 72
C. 96
D. 108
Correct Answer: C. 96
Explanation:
Formula:
6(n − 2)²
6(6 − 2)²
= 6 × 16
= 96
Sample Question 13 – Cube Net Logic
In a cube net, adjacent faces become:
A. Opposite
B. Connected by edge
C. Invisible
D. Corner faces
Correct Answer: B. Connected by edge
Explanation:
Adjacent faces always share a common edge.
Sample Question 14 – Cuboid Properties
Which statement is correct for a cuboid?
A. All edges are equal
B. All faces are squares
C. Opposite faces are equal rectangles
D. It has 10 edges
Correct Answer: C. Opposite faces are equal rectangles
Explanation:
A cuboid contains rectangular faces and opposite faces are equal.
Sample Question 15 – Cube Formula Application
A cube is divided into 3 equal parts along each edge. How many total smaller cubes are formed?
A. 9
B. 18
C. 27
D. 36
Correct Answer: C. 27
Explanation:
Formula:
n³
3³ = 27
Quick Solving Tips for Cube and Cuboid
- Memorize all painted-cube formulas.
- Visualize cubes layer-by-layer.
- Identify corner, edge, and face cubes properly.
- Practice cube rotation mentally.
- Use rough diagrams for clarity.
- Remember opposite-face rules.
- Verify formulas before calculation.
- Practice cube net visualization regularly.
Most Important Areas Asked in Exams
| Topic | Importance Level |
|---|---|
| Painted Cubes | Very High |
| Cube Cutting | Very High |
| Visible Cubes | High |
| Cube Folding | High |
| Opposite Faces | High |
| Cube Rotation | Moderate |
Practice Strategy
- Practice painted cube problems daily.
- Memorize standard formulas.
- Improve 3D visualization ability.
- Practice cube folding questions regularly.
- Solve previous year reasoning questions.
- Draw rough cube diagrams during practice.
Final Takeaway
Sample Questions in Cube and Cuboid help candidates improve spatial visualization, analytical thinking, logical reasoning, and three-dimensional observation ability. Regular practice strengthens cube interpretation skills and improves solving speed significantly.
Strong understanding of painted cubes, cube cutting, visible cubes, cube folding, and face relationships is the key to solving Cube and Cuboid questions effectively in competitive examinations.