Cube and Cuboid: Shapes, Properties, and Examples
Understanding the Difference Between Cube And Cuboid is essential for students, as both are foundational 3D geometric solids with distinct structural characteristics. Distinguishing these shapes helps in solving surface area, volume, and geometry questions in board exams and competitive tests like the JEE.
What a Cube Represents in Geometry
A cube is a three-dimensional solid with six identical square faces, twelve equal edges, and eight vertices. Each angle in a cube is a right angle, making it a regular polyhedron where all sides and faces are congruent.
The volume of a cube with edge length $a$ is:
$V = a^3$
For more clarity on differentiating geometric solids, see Difference Between Square And Rectangle.
Mathematical Meaning of Cuboid
A cuboid is a three-dimensional solid bounded by six rectangular faces, twelve edges, and eight vertices. Not all faces or edges are equal, but opposite faces and opposite edges are always equal in length.
For a cuboid with length $l$, breadth $b$, and height $h$, the volume is:
$V = l \times b \times h$
Cuboids are central to the study of quadrilaterals and their area formulas.
Comparative View of Cube and Cuboid
| Cube | Cuboid |
|---|---|
| All faces are squares | All faces are rectangles |
| All edges are equal in length | Only opposite edges are equal |
| Six congruent faces | Opposite faces are congruent |
| All diagonals (surface and space) are equal | Not all diagonals are equal in length |
| Represents a regular polyhedron | Not a regular polyhedron |
| Three dimensions are always equal ($l = b = h$) | Dimensions can be different ($l \neq b \neq h$) |
| Has higher symmetry | Lower symmetry than cube |
| Diagonal formula is $a\sqrt{3}$ | Diagonal formula is $\sqrt{l^2 + b^2 + h^2}$ |
| Lateral surface area is $4a^2$ | Lateral surface area is $2(l+b)h$ |
| Total surface area is $6a^2$ | Total surface area is $2(lb + bh + lh)$ |
| Volume is $a^3$ | Volume is $l \times b \times h$ |
| Special type of cuboid | General form (includes cube as a case) |
| All internal angles are right angles | All internal angles are right angles |
| Uniform view from every side | Views differ from different sides |
| Used to model equal-sided solids (e.g., dice) | Models typical boxes, bricks |
| Space diagonals are equal for all | Space diagonals could be of two lengths |
| Surface area changes with equal edge | Surface area depends on all dimensions |
| Cube net forms 6 identical squares | Cuboid net forms 3 pairs of rectangles |
| All faces have same area | Opposite faces have equal areas |
| Examples: Dice, Rubik’s cube | Examples: Books, Bricks |
Core Distinctions Between Cube and Cuboid
- Cube has all sides and faces equal
- Cuboid has rectangular faces and unequal sides
- Cube is a regular polyhedron; cuboid is not
- Diagonals in a cube are always equal
- Volume formula: $a^3$ for cube, $lbh$ for cuboid
- Cube models equal-sided solids; cuboid models boxes
Worked Examples
Example 1: Calculate the surface area of a cube with edge length $5$ cm.
$A = 6a^2 = 6 \times 25 = 150\, \text{cm}^2$
Example 2: Find the volume of a cuboid with $l = 4$ cm, $b = 3$ cm, $h = 7$ cm.
$V = lbh = 4 \times 3 \times 7 = 84\, \text{cm}^3$
These examples highlight the practical use of cube and cuboid formulas. Review more in the Difference Between Rectangle And Square article.
Where These Concepts Are Used
- Measuring storage volumes in boxes and containers
- Geometry problems in mathematical olympiads
- Calculating total and lateral surface areas
- Real-world modeling (dice, bricks, packaging)
- Design of square-based structures
Concise Comparison
In simple words, a cube has six equal square faces and equal edges, whereas a cuboid has six rectangular faces with opposite sides equal and varying dimensions.
FAQs on What Is the Difference Between a Cube and a Cuboid?
1. What is the difference between a cube and a cuboid?
A cube and cuboid are both three-dimensional solid shapes, but they differ in the length of their sides and faces.
- A cube has all six faces square and all sides equal in length.
- A cuboid has six rectangular faces, and opposite faces are equal, but its length, breadth, and height can be different.
2. What are the properties of a cube?
A cube is a solid with special characteristics:
- All edges (length, width, height) are equal.
- It has 6 faces, 12 edges, and 8 vertices.
- Each face is a square.
- All angles are right angles (90°).
3. What are the properties of a cuboid?
A cuboid is a 3D rectangle with the following properties:
- It has 6 rectangular faces.
- 12 edges and 8 vertices.
- Opposite faces are equal and parallel.
- Edges opposite each other are equal in length, but length, breadth, and height can differ.
4. How do you calculate the volume of a cube and a cuboid?
The volume of a cube is calculated as side × side × side (s3), and for a cuboid as length × breadth × height.
- Cube: Volume = a × a × a = a3
- Cuboid: Volume = l × b × h
5. How do the faces of a cube differ from those of a cuboid?
The faces of a cube are all squares, while the faces of a cuboid are rectangles.
- In a cube: all six faces are equal-sized squares.
- In a cuboid: faces are in pairs of equal rectangles, but not all must be squares.
6. Is every cuboid a cube? Why or why not?
No, not every cuboid is a cube.
- A cube is a special type of cuboid where all edges are equal and all faces are squares.
- Most cuboids have unequal sides and rectangular faces, so they don't qualify as cubes.
7. Can a cube have rectangular faces?
No, a cube cannot have rectangular faces.
- All faces of a cube must be squares, which means all sides are equal.
- If any face is a rectangle, the shape is a cuboid, not a cube.
8. What are some real-life examples of cubes and cuboids?
Common cubes and cuboids are seen in everyday life:
- Cube examples: Dice, Rubik's Cube, ice cubes.
- Cuboid examples: Bricks, books, matchboxes, shoeboxes.
9. How do the surface area formulas for a cube and a cuboid differ?
The surface area of a cube is 6 × (side)2, and for a cuboid it is 2 × (length × breadth + breadth × height + height × length).
- Cube: Surface Area = 6a2
- Cuboid: Surface Area = 2(lb + bh + hl)
10. Why are cubes considered a special type of cuboid?
A cube is considered a special type of cuboid because all its edges are equal and every face is a square.
- All cubes fit the definition of cuboids (6 faces, 12 edges, 8 vertices).
- However, their equal sides and square faces make them unique among cuboids.
11. List the similarities between a cube and a cuboid.
Cubes and cuboids have several similarities:
- Both have 6 faces, 12 edges, and 8 vertices.
- All angles are right angles (90°).
- Opposite faces are equal and parallel.
- Both are three-dimensional shapes.
