Difference Between Cuboid and Cube
The concept of cuboid and cube plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Mastering the differences, properties, and formulas related to these 3D shapes helps students excel in competitive exams and understand daily measurement tasks effortlessly.
What Is Cuboid and Cube?
A cuboid is a three-dimensional solid figure with six rectangular faces, twelve edges, and eight vertices, where the length, breadth, and height can all be different. A cube is a special type of cuboid where all sides are equal, so every face is a square. You’ll find this concept applied in areas such as 3D shapes, geometry, and daily-life measurements.
| Shape | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 (all squares) | 12 (all equal) | 8 |
| Cuboid | 6 (rectangles) | 12 | 8 |
Primary Difference Between Cuboid and Cube
The main difference: In a cube, all edges are the same length, making every face a perfect square. In a cuboid, the edges can have different lengths, so faces are rectangles.
- Cube: All sides equal (l = b = h), all faces are squares.
- Cuboid: Sides may differ (l ≠ b ≠ h), faces are rectangles.
- Cube is a special type of cuboid where each side matches in size.
| Feature | Cube | Cuboid |
|---|---|---|
| Edge Lengths | All equal | Not all equal |
| Face Shape | Squares | Rectangles |
| Every Cube is a Cuboid? | Yes | No |
Key Formula for Cuboid and Cube
Cube:
- Surface Area: 6 × (side)2
- Volume: (side)3
- Diagonal: side × √3
Cuboid:
- Surface Area: 2(lb + bh + hl)
- Volume: l × b × h
- Diagonal: √(l2 + b2 + h2)
Step-by-Step Illustration: Example Calculation
Example 1: Find the surface area and volume of a cuboid with length 5 cm, breadth 3 cm, height 4 cm.
1. Surface Area = 2(lb + bh + hl) = 2(5×3 + 3×4 + 5×4)2. = 2(15 + 12 + 20) = 2×47 = 94 cm2
3. Volume = l × b × h = 5 × 3 × 4 = 60 cm3
Example 2: Find the volume of a cube with side 7 cm.
1. Volume = (side)3 = 73 = 343 cm3
Real-Life Usage of Cuboid and Cube
- A dice or Rubik’s cube: Cube (all sides are equal and square).
- A book, a brick, a matchbox: Cuboid (faces are rectangles, sizes vary).
- Shipping boxes: Most are cuboids, but small square gift boxes are cubes.
- Fridge, TV: Cuboids in daily life.
Classroom Tip
A quick way to remember: “If all faces are square and the box looks the same from all sides, it’s a cube. If opposite faces are rectangles of equal size but not all sides match, it’s a cuboid.” Vedantu’s teachers often use real objects in the class—like books and dice—to help students visualize these shapes.
Try These Yourself
- Find the surface area of a cube with edge 10 cm.
- Identify 3 items at home that are cuboids.
- If a cuboid has l = 6 cm, b = 2 cm, h = 3 cm, what is its volume?
- Is a refrigerator a cube or a cuboid?
Frequent Errors and Misunderstandings
- Confusing all boxes as cubes (remember: a cube has all sides equal).
- Mixing up surface area and volume formulas between cubes and cuboids.
- Using wrong measurements when sides are not labeled (always check: length, breadth, height).
Relation to Other Concepts
The idea of cuboid and cube connects with understanding squares, rectangles, and 2D–3D relationships. Mastering these shapes helps with surface area and volume topics and supports skills in advanced geometry lessons.
Cross-Disciplinary Usage
Cuboid and cube are not only useful in maths but also play an important role in physics (measuring capacity, density), computer graphics (3D modeling), and logical reasoning. Students preparing for JEE or Olympiads often encounter questions on surface areas and volumes requiring quick formula recall and comparison between these shapes.
Summary Table: Cube vs Cuboid
| Feature | Cube | Cuboid |
|---|---|---|
| Sides | Equal | Can be different |
| Faces | 6 (squares) | 6 (rectangles) |
| Diagonal | side × √3 | √(l² + b² + h²) |
| Volume | side3 | l × b × h |
Internal Links for Deeper Learning
- Difference Between Cube and Cuboid
- Surface Area and Volume of Cube, Cuboid, and Cylinder
- Faces, Edges, and Vertices
- Rectangular Prism (Cuboid)
- Properties of a Cube
We explored cuboid and cube—from meaning, formulas, and comparisons, to daily-life examples and exam tricks. Continue practicing with Vedantu to build confidence in solving all kinds of 3D geometry problems related to cubes and cuboids!
FAQs on Cuboid and Cube: Maths Concept Explained
1. What is the main difference between a cuboid and a cube?
The primary difference lies in their side lengths: a cube has all sides equal in length, while a cuboid has different lengths, breadths, and heights. This difference impacts their surface area and volume calculations.
2. How many faces, edges, and vertices do a cuboid and a cube have?
Both shapes have 8 vertices (corners) and 12 edges (lines where faces meet). However, a cube has 6 identical square faces, whereas a cuboid has 6 rectangular faces, which may or may not be all the same size.
3. What are real-life examples of cuboids and cubes?
A cube's real-world examples include dice, Rubik's Cubes, and some boxes. Cuboids are more common and include bricks, books, shoeboxes, and most rooms.
4. What is the formula for calculating the surface area and volume of a cube and a cuboid?
Cube:
• Surface Area: 6a², where 'a' is the side length.
• Volume: a³
Cuboid:
• Surface Area: 2(lb + bh + lh), where l=length, b=breadth, h=height.
• Volume: lbh
5. Is a dice a cube or a cuboid?
A standard dice is a cube because all its faces are equal squares.
6. How are cubes and cuboids related?
A cube is a special type of cuboid where all its sides are equal in length. All cubes are cuboids, but not all cuboids are cubes.
7. What are the different types of cuboids?
Cuboids can be classified based on their dimensions. A cube is a special type of cuboid with equal side lengths. Other cuboids can have various combinations of unequal lengths, breadths, and heights.
8. How do I calculate the diagonal of a cube and a cuboid?
Cube: Diagonal = a√3, where 'a' is the side length.
Cuboid: Diagonal = √(l² + b² + h²), where l=length, b=breadth, h=height.
9. What are some common mistakes students make when working with cuboids and cubes?
• Confusing surface area and volume formulas.
• Incorrectly identifying a cube vs. a cuboid.
• Miscalculating dimensions in word problems.
• Forgetting units in final answers.
10. How can I visualize the difference between a cuboid and a cube?
Imagine a building block: if all sides are the same size, it's a cube. If the sides are different sizes, it's a cuboid. Using real objects like boxes helps understand this difference.
11. What is the importance of understanding cuboids and cubes in higher-level maths?
Understanding cuboids and cubes is crucial for grasping concepts in geometry, including surface area and volume calculations of more complex 3D shapes and their applications in mensuration problems.
12. Are there any online resources to help me practice solving problems involving cuboids and cubes?
Vedantu provides numerous practice worksheets, interactive exercises and video tutorials to enhance your understanding of cuboids and cubes. These resources cover various difficulty levels and are aligned with exam requirements.
