The key difference between cube and cuboid is: a cube has six square-shaped faces of the same size but a cuboid has rectangular faces. Although both cube and cuboid looks the same in structure they have a few different properties based on edge-length, diagonals and faces.
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 which have some common properties like both have six faces, eight vertices and twelve edges. Also, all the interior angles equal to 90 degrees. Let us see how cubes and cuboid can be differentiated from each other.
Definition of Cube and Cuboid
Cube: A three-dimensional shape which has six square-shaped faces of equal size and has an angle of 90 degrees between them is called a cube. It has 6 faces, 12 edges and 8 vertices. Opposite edges are equal and parallel. Each vertex meets three faces and three edges.
Cuboid: A three-dimensional figure which has three pairs of rectangular faces attached opposite to each other. These opposite faces are the same. Out of these six faces, two can be squares. The other names for cuboid are rectangular boxes, rectangular parallelepipeds, and right prisms.
What are the Differences Between Cube and Cuboid?
|1||Sides||All the side length 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 the six faces of a cube are squares||All the 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 the 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)|
Cube and Cuboid Similarities
- A cube and cuboid have six faces.
- They both have 12 edges.
- Cube and cuboid have eight vertices.
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 = 6a2
= 6× 82 = 6 ×64
= 384 cm2
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