Difference between Cube and Cuboid
In mathematics, we learn about different shapes and figures such as cylinders, squares, cones, rectangles, and much more. Each of these shapes and figures has its own distinct properties and formulas that we use while solving questions related to geometry in mathematics. Two such figures - cube and cuboid are considered as similar but yet different in their properties. Let us see the definition, properties, and differences between cubes and cuboids.
| 1. | Definition of a Cube |
| 2. | Definition of a Cuboid |
| 3. | Properties of a Cube and Cuboid |
| 4. | Difference between a Cube and Cuboid |
| 5. | FAQs on the Difference between a Cube and Cuboid |
Definition of a Cube
A cube is a 3D shape with six square-shaped faces that are all equal in size and has an angle of 90° between them. The cube has 6 faces, 12 edges, and 8 vertices where each vertex meets three faces and three edges. The opposite edges of a cube are equal and parallel to each other.
Below is an image of a cube showcasing its edge, face, and vertex.
Definition of a Cuboid
A cuboid is a box-shaped 3D figure which has three pairs of rectangular faces attached opposite to each other. The shape contains six faces where the opposite faces are equal to each other. Additionally, out of these six faces, two can be squares. The other names for a cuboid are rectangular boxes, rectangular parallelepipeds, and right prisms. In a cuboid, any face can be at the bottom and the remaining four adjacent faces are called the lateral faces of a cuboid.
Below is an image of a cuboid for reference showcasing its height, breadth, and length.
Properties of a Cube and Cuboid
Listed below are the properties of both a cube and a cuboid. Both the shapes have a few similar properties but have many different properties as well.
| Properties of a Cube | Properties of a Cuboid |
|---|---|
| All faces are square-shaped | All faces are rectangle-shaped |
| All faces and edges are equal | Opposite faces and opposite edges are equal |
| The angles are at right angles | The angles are at right angles |
| Each of the faces meets the other adjacent four faces | Two faces meet at the edge |
| The vertices meet three faces and three edges | The intersection of three faces is a vertex |
Difference between a Cube and Cuboid
A cube and a cuboid look very similar to each other in structure but both the shapes have their own properties based on edge, length, diagonals, and faces. The main difference between a cube and a cuboid is that a cube has six square-shaped faces of the same size but a cuboid has rectangular faces. Listed below are the differences between Cube vs Cuboid.
| Cube | Cuboid |
|---|---|
| A 3D shape of a square | A 3D shape of a rectangle |
| The measurement of length, breadth, and height are equal i.e sides/edges are equal | The measurement of length, breadth, and height are not equal i.e. sides/edges are not equal |
| In a cube, all the six faces are squares |
In a cuboid, all six faces are rectangles |
| A cube as 12 diagonals in total with surface area measured the same | A cuboid has 12 diagonals in total where 3 diagonals are different in the measure |
| In a cube, the 4 internal diagonals should have the same measure | In a cuboid, among the 4 internal diagonals, two pairs of the internal angles are of different measurement |
| Rubik's cube, Dice, ice cube are a few examples | Bricks, lunch box, are a few examples of a cuboid |
| Diagonal Formula = √3 × (side) | Diagonal formula = √(length2 + breadth2 + height2) |
| Volume Formula = (Side)3 | Volume Formula = length × breadth × height |
Related Topics
FAQs on the Difference between Cube and Cuboid
What is the Main Difference between a Cube and a Cuboid?
A cube and a cuboid look very similar to each other in structure but both shapes have their own properties based on edge, length, diagonals, and faces. The main difference between a cube and a cuboid is that a cube has six square-shaped faces of the same size but a cuboid has rectangular faces. A cuboid is rectangular-shaped and a cube is square-shaped.
Can Cubes also be Called Cuboids?
Cubes can be called special cuboids, as a cube is a 3D square-shaped figure with all sides i.e. length, breadth, and height equal to each other. The cube has 6 faces, 12 edges, and 8 vertices where each vertex meets three faces and three edges. The opposite edges of a cube are equal and parallel to each other. Whereas a cuboid is a 3D rectangular figure with all sides not equal to each other.
What Shape is a Cuboid?
A cuboid is a box-shaped 3D figure which has three pairs of rectangular faces attached opposite to each other. The cuboid contains six faces where the opposite faces are equal to each other. Additionally, out of these six faces, two can be squares. The other names for a cuboid are rectangular boxes, rectangular parallelepipeds, and right prisms. In a cuboid, any face can be at the bottom and the remaining four adjacent faces are called the lateral faces of a cuboid.
Can a Cube be Called a Square?
No, a square cannot be called a cube since the dimensions of both figures are different. A square is a 2D figure with length and breadth whereas a cube is a 3D figure with length, breadth, and height. A square has four sides and four vertices whereas a cube have 12 sides and 8 vertices.
Can a Cuboid have Two Square Faces?
A cuboid is a 3D rectangular-shaped figure with six rectangular faces where all the faces are either parallel or perpendicular to each other. A figure with six square faces is a cube but a figure with two square faces and four rectangular faces is known as a square cuboid.
What are the Properties of a Cube and a Cuboid?
The properties of a cube and cuboid are:
- Both are 3D square-shaped figures and rectangular-shaped figures respectively
- The faces and edges of a cube are equal whereas opposite faces and edges are equal to each other in a rectangle
- The angles of both a cube and cuboid are at right angles
- In a cube and the cuboid,each of the 8 vertices meets three faces and three edges.