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Cube, and Cuboid both are three-dimensional shapes. Both cube and cuboid look similar, but they can be distinguished only by their properties. Before studying the difference between cube and cuboid. Let us learn about cubes and cuboids and look at their properties. Also, learn about particular properties which differentiate a cube from a cuboid.
Cube
A cube is a three-dimensional shape or simply a block, defined in an XYZ plane, where all the length, height, and breadth are the same. It has eight vertices, six faces, and twelve edges. The face of a cube has a square shape and has equal dimensions. The angles made by a cube are right-angled.
Properties of a cube
- All faces of a cube are square-shaped
- All the angles of a cube are right-angled
- Opposite edges are parallel and equal
- All the diagonals are equal in size
- Intersection of three faces is a vertex
Cuboid
A cuboid is a polyhedron with eight vertices, six faces, and twelve edges. The opposite faces of the cuboid are parallel, equal in area and perimeter. But not all the sides are equal in dimensions. The angles made by a cuboid are right-angled.
Properties of a cuboid
- All faces of a cuboid are rectangular shaped
- Opposite edges are parallel and equal
- All the angles of a cuboid are right-angled
- Opposite faces are equal in area and perimeter
- Intersection of three faces is a vertex
Formulae of cube and cuboid
| Cube | Cuboid |
| Volume of cube = (side)3 | Volume of cuboid = Length x Height x Breadth |
| Total Surface Area= 6 (side)2 | Total Surface Area = 2 (Length x Breadth + Breadth x Height + Breadth x Height) |
| Lateral Surface Area = 4 (side)2 | Lateral Surface Area = 2 x height (length + breadth) |
| Diagonal of a cube = √ 3l | Diagonal of cuboid = √ (l2 + b2 + h2) |
| Perimeter of cube = 12 x side | Perimeter of cuboid = 4 (length + breadth + height) |
Difference between cube and cuboid
| Cube | Cuboid |
| It is a 3 – dimensional shape of a square | It is a 3 – dimensional shape of a rectangle. |
| Diagonals on the surface are of the same length | Of the 12 diagonals, 3 diagonals are of different measure. |
| All six faces are square in shape. | All six faces are rectangle in shape. |
| Internal diagonals are of equal length. | Two pairs of internal diagonals are of different lengths. |
| Examples: Rubik’s cube, Dice. | Examples: Construction bricks, Pencil box. |
Problems on a cube and cuboid
- Calculate the volume of a cube, if one of its sides is of length 4m.
Given the length of side = 4m
Volume of a cube = a x a x a = 4 x 4 x 4 = 64 m3.
- Find the surface area of a cube, if one of its sides is of length 2m.
Given length of a side = 2m
Surface area of cube = 6 x a x a = 6 x 2 x 2 = 24 m2.
- Find the total surface area of a cuboid with dimensions, l = 2 cm, b = 3 cm and h = 4 cm.
Total surface are of a cuboid = 2 (lb + bh + lh) = 2 (2×3 + 3×4 + 4×2)
= 2 (6 + 12 + 8)
= 2 x 26 = 2=56 cm2.
- Find the lateral surface area of a cuboid with dimensions that are 3cm, 3cm, and 2cm.
Given, Length of cuboid = 3cm,
Breadth of cuboid = 3cm,
Height of cuboid = 2cm
Lateral surface area of a cuboid = 2h (l + b)
= 2 x 2 (3 + 3) = 4 (6) = 24 cm2.
Conclusion
Cube and Cuboid both are basic three-dimensional shapes. They both may visually look the same, but it is important to learn their properties to distinguish them. Every three-dimensional shape has its particular properties, learning about them, will help us to identify or calculate problems. In this article, we studied cube, cuboid, their properties, and some problems on them to understand the concept.
