Cube and cuboid are three-dimensional shapes which consist of six faces, eight vertices and twelve edges. Both the shapes looks the same but have different properties. The area and volume of cube, cuboid and also cylinder differ with each other.
In everyday life, objects like a wooden box, a matchbox, a tea packet, a chalk box, a dice, a book etc are encountered. All these objects have a similar shape. In fact, all these objects are made of six rectangular planes. The shape of these objects is either a cuboid or cube. Here, in this article, we will learn the difference between the two shapes with the help of their properties and formulas of surface area and volume.
Table of contents:
- Properties of Cuboid
- Properties of Cube
- Example Questions
- Video Lesson
Definition of Cube and Cuboid
Cube: A cube is a three-dimensional shape which is defined XYZ plane. It has six faces, eight vertices and twelve edges. All the faces of the cube are in square shape and have equal dimensions.
Cuboid: A cuboid is also a polyhedron having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel and equal in dimensions. But not all the faces of a cuboid are equal in dimensions.
Shape of Cube and Cuboid
As we already know both cube and cuboid are in 3D shape, whose axes goes along the x-axis, y-axis and z-axis plane. Now let us learn in detail.
A cuboid is a closed 3-dimensional geometrical figure bounded by six rectangular plane regions.
Properties of a Cuboid
Faces of Cuboid
A Cuboid is made up of six rectangles, each of the rectangles is called the face. In the figure above, ABFE, DAEH, DCGH, CBFG, ABCD and EFGH are the 6 faces of cuboid.
The top face ABCD and bottom face EFGH form a pair of opposite faces. Similarly, ABFE, DCGH, and DAEH, CBFG are pairs of opposite faces. Any two faces other than the opposite faces are called adjacent faces.
Consider a face ABCD, the adjacent face to this are ABFE, BCGF, CDHG, and ADHE.
Base and lateral faces
Any face of a cuboid may be called as the base of the cuboid. The four faces which are adjacent to the base are called the lateral faces of the cuboid. Usually, the surface on which a solid rest on is known to be the base of the solid.
The edge of the cuboid is a line segment between any two adjacent vertices.
There are 12 edges, they are AB,AD,AE,HD,HE,HG,GF,GC,FE,FB,EF and CD and the opposite sides of a rectangle are equal.
Hence, AB=CD=GH=EF, AE=DH=BF=CG and EH=FG=AD=BC.
Vertices of Cuboid
The point of intersection of the 3 edges of a cuboid is called the vertex of a cuboid.
A cuboid has 8 vertices A, B, C, D, E, F, G and H represents vertices of the cuboid in fig 1.
By observation, the twelve edges of a cuboid can be grouped into three groups such that all edges in one group are equal in length, so there are three distinct groups and the groups are named as length, breadth and height.
Properties of Cube
- A cube has three faces and three edges of equal length.
- It has square-shaped faces.
- The angles of the cube in the plane are at a right angle.
- Each face of the cube meets four other faces.
- Each vertex of the cube meets three faces and three edges.
- Opposite edges of the cube are parallel to each other.
Cube and Cuboid Formula
Surface Area of Cube and Cuboid
The surface area of a cuboid is equal to the sum of the areas of its six rectangular faces.
Consider a cuboid having the length to be ‘l’ cm, breadth be ‘b’ cm and height be ‘h’ cm.
- Area of face EFGH = Area of Face ABCD = (l× b) cm2
- Area of face BFGC = Area of face AEHD = (b ×h) cm2
- Area of face DHGC = Area of face ABFE = (l ×h) cm2
Total surface area of a cuboid = Sum of the areas of all its 6 rectangular faces
|Total Surface Area of Cuboid= 2(lb + bh +lh)|
Lateral surface area of a Cuboid:
The sum of surface areas of all sides except the top and bottom face of solid is defined as the lateral surface area of a solid.
Consider a Cuboid of length, breadth and height to be l, b and h respectively.
Lateral surface area of the cuboid= Area of face ADHE + Area of face BCGF + Area of face ABFE + Area of face DCGH
=2(b × h) + 2(l × h)
=2h(l + b)
|LSA of Cuboid = 2h(l +b)|
Surface Area of a Cube:
For cube, length = breadth = height
Suppose the length of an edge = l
Hence, surface area of the cube = 2(l × l +l × l + l × l) = 2 x 3l2 = 6l2
|Total Surface Area of Cube= 6l2|
Lateral surface area of a Cube:
Formula to find Lateral surface area of the cube is:
2(l × l + l × l) = 4l2
|LSA of Cube = 4l2|
Volume of the Cube and Cuboid
Volume of Cuboid:
The volume of the cuboid is equal to the product of the area of one surface and height.
Volume of the cuboid = (length × breadth × height) cubic units
|Volume of the cuboid = ( l × b × h) cubic units|
Volume of the Cube:
The volume of the cube is equal to the product of the area of the cube and height. As we know already, all the edges of the cube are of same length. Hence,
Volume of the cube = l2 × h
Since, l = h
Volume of the cube = l2 × l
|Volume of the cube = l3|
Diagonal of Cube and Cuboid
The length of diagonal of the cuboid is given by:
Diagonal of the cuboid =√( l2 + b2 +h2)
The length of diagonal of cube is given by:
Perimeter of Cube and Cuboid
The perimeter of cuboid will be based on its length, width and height. Since the cuboid has 12 edges and the value of its edges are different from each other, therefore, its perimeter is given by:
Perimeter of a cuboid = 4 (l + b + h)
where, l is the length
b is the breadth
h is the height
The perimeter of the cube also depends upon a number of edges it has and the length of the edges. Since the cube has 12 edges and all the edges have equal length, therefore the perimeter of the cube is given by:
Perimeter of a cube = 12l
where l is the length of the edge of the cube.
Let us summarise all the formulas in a table.
|Surface Area||6l2||2(lb + bh +lh)|
|Lateral Surface Area||4l2||2h(l +b)|
|Volume||l3||l × b × h|
|Diagonal Length||√3l||√( l2 + b2 +h2)|
|Perimeter||12l||4 (l + b + h)|
Example 1: Find the total surface area of cuboid with dimensions 2 inches × 3 inches × 7 inches.
Solution: Total Surface Area(TSA) = 2 (lb + bh + hl )
TSA = 2 ( 2×3 + 3×7 + 7×2)
TSA = 2 ( 6 + 21 + 14 )
TSA = 82
So, the total surface area of this cuboid is 82 inches2
Example 2: The length, width and height of a cuboid are 12 cm, 13 cm and 15 cm respectively. Find the lateral surface area of a cuboid.
Solution: Lateral surface area of a cuboid is given by:
LSA = 2h ( l + w )
LSA = 2×15 ( 12 + 13 )
LSA = 750 cm2
Example 3: Find the surface area of a cube having its sides equal to 8 cm in length.
Solution: Given length, ‘a’= 8 cm
Surface area = 6a2
= 6× 82 = 6 ×64
= 384 cm2
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Frequently Asked Questions
What the difference between cuboid and cube?
A cube is a three-dimensional figure whose all sides are equal i.e. all of its 6 faces are square. On the contrary, a cuboid is a three-dimensional figure whose all sides are not equal and all of its 6 faces are rectangles.
What are the formulas of cube and cuboid?
- Total surface area:
Cube= 6× (side)2
Cuboid= 2(lb + bh +lh)
- Lateral surface area:
Cube= 4× (side)2
Cuboid= 2h(l +b)
Cuboid= (length × breadth × height)
Is a cube a special kind of cuboid?
Yes, a cube is a special kind of cuboid where all the faces of the cuboid are of equal length. In a cuboid, there are 6 faces which are rectangles. If the rectangles have equal sides, they become squares and eventually, the cuboid becomes a cube.