Difference Between Cube and Cuboid
Both cube and cuboid are three-dimensional (3D) solid shapes, but they differ in dimensions and properties.
🔹 1. Definition
✅ Cube
A cube is a 3D solid in which all sides (length, breadth, height) are equal.
👉 All faces are squares.
📦 Practical Examples:
Dice (Ludo dice)
Ice cubeRubik’s Cube
Sugar cube
Cuboid
A cuboid is a 3D solid in which length, breadth, and height may be different.
👉 All faces are rectangles.
📦 Practical Examples:
Book
BrickMatchbox
Mobile phone box
Room
🔹 2. Comparison Table
| Feature | Cube | Cuboid |
|---|---|---|
| Shape of faces | All square | All rectangular |
| Number of faces | 6 | 6 |
| Number of edges | 12 | 12 |
| Number of vertices | 8 | 8 |
| Dimensions | l = b = h | l ≠ b ≠ h (generally) |
| Special case | A cube is a special type of cuboid | General rectangular solid |
👉 Important: Every cube is a cuboid, but every cuboid is not a cube.
🔹 3. Important Formulas (Very Important for Exams 🔥)
Cube Formulas
Let side = a
Volume = a³
Total Surface Area (TSA) = 6a²
Lateral Surface Area (LSA) = 4a²
Diagonal of cube = √3 a
Cuboid Formulas
Let length = l, breadth = b, height = h
Volume = l × b × h
Total Surface Area (TSA) = 2(lb + bh + hl)
Lateral Surface Area (LSA) = 2h(l + b)
Diagonal of cuboid = √(l² + b² + h²)
🔹 4. Practical Numerical Example
Example 1: Cube
A dice has side = 4 cm
👉 Volume = 4³ = 64 cm³
👉 TSA = 6 × 4² = 96 cm²
Example 2: Cuboid
A book has dimensions 10 cm × 6 cm × 4 cm
👉 Volume = 10 × 6 × 4 = 240 cm³
👉 TSA = 2(60 + 24 + 40)
= 2(124) = 248 cm²
5. Visual Understanding
If all dimensions same → Cube
If dimensions different → Cuboid
🔥 Exam Important Points (SSC, NDA, NTSE, JKSSB)
✔ Volume ratio of cube with sides a : b = a³ : b³
✔ Surface area ratio = a² : b²
✔ Diagonal formula is commonly asked in MCQs
✔ Cube maximizes volume for given surface area (conceptual question