The key difference between a cube and a cuboid is: a cube has six square-shaped faces of the same size but a cuboid has rectangular faces. Although both cubes and cuboids look the same in structure they have a few different properties based on edge length, diagonals, and faces. Join Safalta School Online and prepare for Board Exams under the guidance of our expert faculty.
In Geometry, there are many shapes such as cylinder, sphere, and cone that has distinct properties but only cuboid and cube are two such solids that have some common properties both have six faces, eight vertices and twelve edges.
Also, all the interior angles are equal to 90 degrees.
Let us see how cubes and cuboid can be differentiated from each other.
Definition of Cube and Cuboid
Cube:
A cube is a three-dimensional geometric shape that has six square faces of equal size.
All of its edges have the same length, and all of its angles are right angles (90 degrees).
In other words, all sides of a cube are congruent, and all angles within the cube are equal.
A cube can be thought of as a special type of cuboid where all dimensions are equal.
Cuboid:
A cuboid, also known as a rectangular prism, is a three-dimensional geometric shape with six rectangular faces.
Unlike a cube, the faces of a cuboid can have different sizes, and its edges may have different lengths.
The angles between the faces of a cuboid can be right angles (90 degrees), acute angles (less than 90 degrees), or obtuse angles (greater than 90 degrees).
Essentially, a cuboid has three pairs of equal dimensions: length, width, and height.
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What are the Differences Between Cube and Cuboid?
| S.No | Topics | Cube | Cuboid |
| 1 | Sides | All the side lengths of a cube are of equal measure | All the side length of a cuboid are of different measure |
| 2 | Shape | A cube is a three-dimensional form of a square | A cuboid is a three-dimensional form of a rectangle |
| 3 | Faces | All six faces of a cube are squares | All six faces of a cuboid are rectangles |
| 4 | Diagonals | The 12 diagonals on the cube surface are of the same measure. | A cuboid has 12 diagonals. Among the set of 4 diagonals, 3 diagonals of a cuboid are of different measures |
| 5 | Internal Diagonals | The total of 4 internal diagonals should have the same measure | A cuboid also has 4 internal diagonals. Among that, the two pairs of internal angles are of different measures |
| 6 | Example | Rubik’s Cube, Dice Ice cube | Duster, Bricks |
| 7 | LSA (Lateral Surface Area) Formula | 4 × (Side) 2 | 2 (length + breadth) height |
| 8 | TSA (Total Surface Area) Formula | 6 × (side) 2 | 2 [(length.breadth) + (breadth.height) + (height.length)] |
| 9 | Diagonal Formula | √3 × (side) | √(length2 + breadth2 + height2), |
| 10 | Volume Formula | (Side)3 | length × breadth × height |
| 11 | Perimeter Formula | 12(Side) | 4(length + breadth + height) |
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Cube and Cuboid Similarities
- A cube and cuboid have six faces.
- They both have 12 edges.
- Cube and cuboid have eight vertices.
Solved Examples
Example 1: Determine the total surface area of cuboid that has length = 2 cm, breadth = 3 cm and height = 7 cm.
Solution: Total Surface Area(TSA) of cuboid = 2 (lb + bh + hl )
TSA = 2 ( 2×3 + 3×7 + 7×2)
TSA = 2 ( 6 + 21 + 14 )
TSA = 82
Therefore, the total surface area of this cuboid is 82 sq.cm.
Example 2: Calculate the surface area of a cube with edge length equal to 8 cm.
Solution: Given length, ‘a’= 8 cm
Surface area = 6a square
= 6× 82 = 6 ×64
= 384 cm square
