Cuboid
A cuboid is a threedimensional geometric shape that looks like a book or a rectangular box. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height. Sometimes the cuboid shape is confused with a cube since it shares some properties of a cube, however, they are different from each other.
Cuboids are commonly used in everyday life in the form of packaging boxes, building materials (such as bricks), electronic devices (such as mobiles and tablets), etc. Thus, it is very important to study about the cuboids and formulas related to volume and surface area of cuboids.
1.  What is a Cuboid? 
2.  Cuboid Faces Edges Vertices 
3.  Cuboid Formulas 
4.  Cuboid Properties 
5.  Cuboid Net 
6.  FAQs on Cuboid Shape 
What is a Cuboid?
We know that a rectangle is a twodimensional shape that has 4 sides. Now, imagine a shape that is formed when many congruent rectangles are placed one on top of the other. The shape thus formed is called a cuboid. Observe the following cuboid which shows its three dimensions: length, width, and height.
A cuboid is also known as a "rectangular prism" or a "rectangular parallelepiped".
Dimensions of a Cuboid
It should be noted that there is no strict rule according to which an edge of a cuboid shape should be named as its length, width (breadth), or height. However, it is understood that if a cuboid is placed on a flat table, then
 the height represents the length of any vertical edge;
 the length is taken to be the larger of the two dimensions of the horizontal face of the cuboid, and
 the width is the smaller of the two dimensions.
These dimensions of a cuboid are denoted by 'l' for length, 'w' for width (breadth), and 'h' for height. Apart from these, the face of a cuboid is the flat surface; the edge is the line segment connecting two adjacent vertices, and the vertex is a point at which two or more edges meet.
Diagonals of a Cuboid
Since a cuboid is a 3D shape, there are two types of diagonals in it:
 Face Diagonals
 Space Diagonals
Observe the following figure which shows a face diagonal and a space diagonal of a cuboid.
Face Diagonal
Face diagonals can be drawn by connecting the opposite vertices on a particular face of a cuboid and we know that only two diagonals can be drawn on one face of a cuboid. Since a cuboid has 6 faces, a total of 12 face diagonals can be drawn in a cuboid.
Space diagonal
A space diagonal is a line segment that joins the opposite vertices of a cuboid. The space diagonals pass through the interior of the cuboid. Therefore, 4 space diagonals can be drawn inside it.
Cuboid Faces Edges Vertices
Every 3D shape has a definite number of faces, edges, and vertices. A cuboid shape has 6 faces, 12 edges, and 8 vertices.
 6 faces: A cuboid has 4 lateral faces and 2 faces of top and bottom. All are in the shape of rectangles. Every two opposite faces are congruent and parallel to each other.
 12 edges: It has 12 edges that include 8 edges of the top and bottom faces and 4 edges that connect them.
 8 vertices: It has 8 vertices which are the vertices of the top and bottom faces. At each vertex, three segments meet from all three dimensions.
Cuboid Formulas
Considering the three main dimensions of a cuboid to be the length (l), width (w), and height (h), observe the basic formulas of a cuboid shape in the following table.
Property of Cuboid  Formula 

Base/Top Diagonals  √(l^{2} + w^{2}) units 
Space Diagonals  √(l^{2} + w^{2} + h^{2}) units 
Perimeter  4(l + w + h) units 
Volume  (l × w × h) cubic units 
Surface Area (or Total Surface Area, TSA) 
2(lw + wh + lh) square units 
Lateral Surface Area, LSA  2h (l + w) square units 
Surface Area of Cuboid
The total area occupied by a cuboid shape is considered the surface area of a cuboid. Since a cuboid is a 3D figure, the surface area will depend on the length, breadth, and height. It can have two kinds of surface areas  Total surface area and lateral surface area. Hence, the formulae to find the surface area of a cuboid are given below:
Total Surface Area of Cuboid, TSA = 2 (lb + bh + lh) square units
Lateral Surface Area of Cuboid, LSA = 2h (l + b) square units
where,
 l = Length,
 b = Breadth,
 h = Height
Volume of Cuboid
The volume of a cuboid is considered the space occupied inside a cuboid. A cuboid's volume depends on its length, breadth, and height. Hence, changing any one of these quantities changes the volume of the shape. The unit of the cuboid's volume is given as the cubic units. Therefore, the formula to calculate the volume of a cuboid is:
Volume of a Cuboid = Base Area × Height
The base area for cuboid = l × b
Hence, the volume of a cuboid, V = l × b × h = lbh cubic units.
where,
 l = Length
 b = Breadth, and
 h = Height
Cuboid Properties
The important properties of a cuboid help us to identify a cuboid shape easily. They are as follows:
 A cuboid has 6 faces, 8 vertices, and 12 edges.
 All the angles formed at the vertices of a cuboid are right angles.
 All the faces are rectangular in shape.
 Any two opposite faces are parallel and congruent to each other.
 Two diagonals can be drawn on each face of a cuboid.
 The opposite edges are parallel to each other.
 A cuboid has 3 dimensions: length, width, and height.
Cuboid Net
The net of a cuboid is referred to when the 3D shape opens or unfolds into a flat object making it into a 2D shape. This view of the cuboid shape helps in identifying the sides that are rectangular in shape. Once the flattened shape is folded back together, the shape of a cuboid is formed. Hence, the cuboid net helps in understanding the cuboid shape better.
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Examples of Cuboid

Example 1: Find the surface area of a cuboid that has dimensions of 8 × 6 × 4 units.
Solution:
The surface area of a cuboid formula = 2(lw + wh + lh)
From the given dimensions, let us take length (l) = 8 units and width (w) = 6 units, and height (h) = 4 units.
Therefore, the surface area = 2 {(8 × 6) + (6 × 4) + (8 × 4)}
= 2 (48 + 24 + 32)
= 2 (104) = 208 square units
Answer: The required surface area is 208 square units.

Example 2: Find the length of the diagonal of a cuboid whose dimensions are 5 × 4 × 3 units.
Solution:
The length of the diagonal of a cuboid formula is: √(l^{2} + w^{2} + h^{2}).
Given length (l) = 5 units, width (w) = 4 units and height (h) = 3 units.
Therefore, the length of diagonal = √(5^{2} + 4^{2} + 3^{2})
= √(25 + 16 + 9)
= √50 units
Answer: The length of the diagonal is √50 units.

Example 3: David has a cuboidal box of dimensions 12 × 7 × 5 inches. What is the volume of the box?
Solution:
The volume of cuboid formula = length × width × height.
By substituting the given values, we get,
Volume = 12 × 7 × 5 = 420 cubic units
Answer: The volume of the box is 420 cubic inches.
FAQs on Cuboid Shape
What is a Cuboid Shape?
A cuboid is a threedimensional shape that has 6 faces, 12 edges, and 8 vertices. It is different from a cube since all the faces of a cuboid are rectangular in shape, whereas, a cube has square faces. The three dimensions of a cuboid are its length, width, and height.
What is the Meaning of Cuboid and Why is the Name?
The word "cuboid" comes from the Latin words "cubus" (meaning cube) and "oid" (meaning like). It means cuboid is a cubelike shape (but it is not cube as it is made of rectangles, not squares).
How Many Edges a Cuboid has?
A cuboid has 12 edges, 6 faces, and 8 vertices.
What is the Net of a Cuboid?
The net of a cuboid is the 2D shape formed by unfolding its faces. If we join the net by joining its edges, we will get a cuboid.
What are the Dimensions of a Cuboid?
A cuboid is a 3D shape that has three dimensions: length, width, and height. If a cuboid has a length of 6 units, a width of 4 units, and a height of 3 units, then its dimensions can be written as: 6 units × 4 units × 3 units.
How to Find the Volume of a Cuboid?
To calculate the volume of a cuboid we find the product of its length, width, and height. It is given by the formula: Volume = length × width × height; and the answer is expressed in cubic units.
What is Lateral Surface Area of Cuboid?
The lateral surface area of a cuboid is the total area of all four lateral faces of the cuboid shape. It is calculated using the formula: 2h(l + b) square units, where l = length, b = breadth, and h = height of the cuboid.
How to Find the Surface Area of a Cuboid?
The surface area of a cuboid is calculated by adding up the areas of all the faces of a cuboid. If 'l' is the length, 'w' is the width and 'h' is the height of the cuboid, then the total surface area of a cuboid is: 2 (lw + wh + lh), which is expressed in square units.
What is the Difference Between Cube and Cuboid?
Both cube and cuboid have the same number of faces, edges, and vertices. All cubes can be considered as cuboids, but all cuboids are not cubes. Cubes have all edges of equal lengths, but in a cuboid, opposite sides are equal and parallel on a face. This is the main difference between a cube and a cuboid. A cube has 6 square faces, while a rectangle has 6 rectangular faces.
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