Cube and cuboid are threedimensional shapes that consist of six faces, eight vertices and twelve edges. The primary difference between them is a cube has all its sides equal whereas the length, width and height of a cuboid are different. Both shapes look almost the same but have different properties. The area and volume of cube, cuboid and also cylinder differ from each other.
In everyday life, we have seen many objects like a wooden box, a matchbox, a tea packet, a chalk box, a dice, a book, etc. All these objects have a similar shape. All these objects are made of six rectangular planes or square planes. In mathematics, the shape of these objects is either a cuboid or a cube. Here, in this article, we will learn the difference between cube and cuboid shapes with the help of their properties and formulas of surface area and volume.
The cube and cuboid shapes in Maths are threedimensional shapes. The cube and cuboid are obtained by giving a thickness to the 2D square and rectangle respectively.
Hence, cube and cuboid shapes have six faces, eight vertices and twelve edges.
The difference between the cube and cuboid shapes are as follows:
As we already know, both cube and cuboid are in 3D shape, whose axes go along the xaxis, yaxis and zaxis. Now, let us learn in detail.
A cuboid is a closed 3dimensional geometrical figure bounded by six rectangular plane regions.
Cuboid Shape
Below are the properties of the cuboid, its faces, base and lateral faces, edges and vertices.
Faces of Cuboid
Base and lateral faces
Edges
Vertices of Cuboid
The formulas for cube and cuboid shapes are defined based on their surface areas, lateral surface areas and volume.
The surface area of a cuboid is equal to the sum of the areas of its six rectangular faces.
Cube and Cuboid Formula
Consider a cuboid having the length to be ‘l’ cm, breadth be ‘b’ cm and height be ‘h’ cm.
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)
Example: If the length, breadth and height of a cuboid are 5 cm, 3 cm and 4 cm, then find its total surface area.
Given, Length, l = 5 cm, Breadth, b = 3 cm and Height, h = 4 cm.
Total surface area (TSA) = 2(lb + bh + lh)
= 2(5 × 3 + 3 × 4 + 5 × 4)
= 2(15 + 12 + 20)
= 2(47)
= 94 sq.cm.
The sum of surface areas of all faces except the top and bottom face of a 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)
Example: If the length, breadth and height of a cuboid are 5 cm, 3 cm and 4 cm, then find its lateral surface area.
Given, Length = 5 cm, Breadth = 3 cm and Height = 4 cm
LSA = 2h(l + b)
LSA = 2 × 4(5 + 3)
LSA = 2 × 4(8)
LSA = 2 × 32 = 64 cm^{2}
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 3l^{2} = 6l^{2}
Total Surface Area of Cube= 6l^{2}
Example: If the length of the side of the cube is 6 cm, then find its total surface area.
Given, side length = 6 cm
TSA of cube = 6l^{2}
TSA = 6 (6)^{2}
TSA = 6 × 36
TSA = 216 sq.cm
Formula to find the Lateral surface area of the cube is: 2(l × l + l × l) = 4l^{2}
LSA of Cube = 4l^{2}
Example: If the length of the side of the cube is 6 cm, then find its lateral surface area.
Given,
Side length, l = 6 cm
LSA of cube = 4l^{2}
LSA = 4 (6)^{2}
LSA = 4 x 36 = 144 sq.cm
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
Example: If the length, breadth and height of a cuboid are 5 cm, 3 cm and 4 cm, then find its volume.
Given, Length (l) = 5 cm, Breadth (b) = 3 cm and Height (h) = 4 cm
Volume of cuboid = l × b × h
V = 5 × 3 × 4
V = 60 cubic cm
Volume of the Cube:
The volume of the cube is equal to the product of the area of the base of a cube and its height. As we know already, all the edges of the cube are of the same length. Hence,
Volume of the cube = l^{2} × h
Since, l = h
Therefore,
Volume of the cube = l^{2} × l
Volume of the cube = l^{3} cubic units
Example: If the length of the side of the cube is 6 cm, then find its volume.
Given, side length = 6 cm
Volume of cube = side^{3}
V = 6^{3}
V = 216 cubic cm
Diagonal of Cube and Cuboid
The length of diagonal of the cuboid is given by:
Diagonal of the cuboid =√( l^{2 }+ b^{2} +h^{2})
The length of diagonal of a cube is given by:
Diagonal of a cube = √3l
Perimeter of Cube and Cuboid
The perimeter of the cuboid is 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, the 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
Example: If the length, width and height of a cuboid are 5 cm, 3 cm and 4 cm, find its Perimeter.
Given, Length = 5 cm, Width = 3 cm and Height = 4 cm
Perimeter = 4 (l + b + h) = 4 (5 + 3 + 4)
P = 4 (12)
P = 48 cm
The perimeter of the cube also depends upon the number of edges it has and the length of the edges. Since the cube has 12 edges and all the edges have equal length, the perimeter of the cube is given by:
Perimeter of a cube = 12l
where l is the length of the edge of the cube
Example: If the side length of the cube is 6 cm, then find its perimeter.
Given , l = 6 cm
The perimeter of cube = 12l
P = 12 × 6
P = 72 cm
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