Cuboid Definition
A cuboid is a convex polyhedron having six rectangular faces, eight vertices, and twelve edges defined in geometry. It's a three-dimensional shape with x, y, and z axes. In mathematics, we can see rectangular cuboid, rectangle box, right rectangle prism, right cuboid, rectangular parallelepiped, and rectangular hexahedron as alternative shapes that are precisely the same as a cuboid. In this article we will learn about cuboid, what is a cuboid shape, all formulas related to cuboid along a few solved examples.
Cuboid Shape
The cuboid shape is a closed three-dimensional figure surrounded by rectangular face or planar areas of rectangles. The figure of cuboid is shown below.
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Example of Cuboid
A solid figure with six rectangular faces that are perpendicular to each other. Following are the example of cuboid:
The lunch box.
Bricks.
Shoebox.
Book.
Fridge
Faces, Edges and Vertices of Cuboid
A cuboid is made up of six faces, eight vertices, and twelve edges. All of these can be represented using the notation shown below:
Faces: There are six rectangular faces to a Cuboid. The six faces in the diagram above are:
ABFE
DAEH
DCGH
CBFG
ABCD
EFGH
ABCD and EFGH are the two opposite and parallel faces of the provided cuboid (top and bottom faces respectively)
CBFG, ABFE, DCGH, and DAEH (opposite and parallel faces which are adjacent to top and bottom faces of the cuboid)
The remaining faces can be written as neighbouring faces to each face, such as ABCD being adjacent to ABFE, BCGF, CDHG, and ADHE.
Edges: The edges of the cuboid relate to the sides of all the rectangular faces. A cuboid, as we all know, has 12 edges. AB, AD, AE, HD, HE, HG, GF, GC, FE, FB, EF, and CD, to name a few. A rectangle's opposite sides are also equal. As a result
AB = CD = GH = EF
AE = DH = BF = CG
EH = FG = AD = BC
Vertices: A cuboid's vertex is the point where the three edges of the cuboid intersect, and a cuboid has eight vertices.
The eight vertices of the provided cuboid form are A, B, C, D, E, F, G, and H.
Consider the representation of a cuboid's faces, edges, and vertices.
3d shape of a cuboid is shown below:
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Cuboid Surface Area
Any three-dimensional shape's surface area is the total area covered by all of its faces. Similarly, a cuboid's surface area is the total of the areas of all of its six rectangular faces. There are two forms of surface area for cuboids: lateral surface area and total surface area. The formulas for these can be found in the diagram below.
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Let length be l, breadth be b, and height be h of a cuboid.
From the figure given above,
Length of AB = CD = EF = GH will be l
Length of BC = AD = EH = FG will be b
Length of CG = BF = AE = DH will be h
Cuboid Lateral Surface Area
A cuboid's lateral surface area (LSA) is the sum of the areas of all faces except the top and bottom.
Lateral Surface Area of the Cuboid
It will be sum of (Area of face ADHE + Area of face BCGF + Area of face ABFE + Area of face DCGH)
= (ADxDH)+(BCxCG)+(ABxBF)+(CDxBC)
= (bxh)+(bxh)+(lxh)+(lxh)
= 2(b × h) + 2(l × h)
= 2h(l + b)
Hence, lateral Surface Area (LSA) = 2h(l + b) sq.units
Cuboid Total Surface Area
A cuboid's total surface area (TSA) is the sum of the areas of all its rectangular faces.
Total Surface Area (TSA) will be 2(lb + bh + hl) sq.units
Cuboid Volume
The volume of a solid is equal to the sum of its base area and height. As a result, the cuboid's volume is equal to the product of its base rectangular face and its height.
Volume = (Length × Breadth) × Height
= (l × b) × h
= lbh
Hence, Volume (V) will be (l × b × h) cubic units
Cuboid Diagonal
The formula for determining the length of the diagonal of a cuboid with dimensions l, b, and h is:
Diagonal = \[\sqrt{l^{2}+b^{2}+h^{2}}\]
Cuboid Perimeter
The sum of the lengths of all the edges will be the perimeter of a cuboid.
The perimeter (P) is equal to 4(l + b + h) units.
Cuboid All Formulas
The table below shows the formulas of a cuboid where we consider length as (l), breadth as (b) and height as (h).
Solved Examples
1. Find the Volume of a Cuboid of Length 10 cm, Breadth 7 cm and Height 5cm.
Solution:
Given,
Length = l = 10 cm
Breadth = b = 7 cm
Height = h = 5 cm
Volume = lbh
= 10 × 7 × 5
= 350 cm3
2. Calculate the Lateral and Total Surface Area of a Cuboid of Dimensions 10 cm × 7 cm × 4 cm.
Solution:
Given dimensions of a cuboid are 10 cm × 7 cm × 4 cm.
i.e. l = 10 cm, b = 7 cm, h = 4 cm
We know formula of Lateral surface area (LSA) of cuboid = 2h(l + b)
= 2 × 4 (10 + 7)
= 8 × 17
= 136 cm2
We know formula of total surface area (TSA) of cuboid = 2(lb + bh + hl)
= 2(10 × 7 + 7 × 4 + 4 × 12)
= 2(70 + 28 + 48)
= 292 cm2
Conclusion
Above we have discussed cuboid shapes, all the important formulas. We can say a cuboid is a rectangular prism or a parallelepiped with 90° vertices. We can conclude the following properties of Cuboid:
It has 12 edges
It has 8 corners or vertices
It has 6 faces.
The cuboid's faces are all rectangle-shaped.
A cuboid's angles are all right angles.
The edges opposite to each other are parallel.
FAQs on Cuboid
1. Define Cuboid.
Ans: A polyhedron with six faces, eight vertices, and twelve edges is known as a cuboid. The cuboid's faces are parallel. A cuboid's faces, on the other hand, are not all the same size.
2. Write the Formula to Find the Area of a Cuboid?
Ans: To find the total surface area of a cuboid, add the areas of all six faces. If the length, breadth, and height of a cuboid are l, b, and h, then the total surface area is 2(lb + bh + hl).
3. Is a Cube a Special Kind of Cuboid?
Ans: Yes, a cube is a special type of cuboid in which all of the cuboid's faces are the same length. There are six faces to a cuboid, all of which are rectangles. If the rectangles have the same number of sides, they become squares, and the cuboid eventually forms a cube.
