Cuboid
A cuboid is a threedimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height. Sometimes a cuboid is confused with a cube since it shares some properties of a cube, however, they are different from each other.
1.  What is a Cuboid? 
2.  Cuboid Formulas 
3.  Properties of a Cuboid 
4.  Surface Area of Cuboid 
5.  Volume of Cuboid 
6.  FAQs on Cuboid Basics 
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.
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 flat on a 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.
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 in the following table.
Face 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  2(lw + wh + lh) square units 
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
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.
Properties of a Cuboid
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 of a cuboid are rectangular in shape.
 Two diagonals can be drawn on each face of a cuboid.
 The opposite edges of a cuboid are parallel to each other.
 The dimensions of a cuboid are length, width, and height.
Surface Area of Cuboid
The total area occupied by a cuboid is considered as 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 formulas to find the surface area of cuboid are given below:
Total Surface Area of Cuboid, S = 2 (lb + bh + lh) square units
Lateral Surface Area of Cuboid, L = 2h (l + b) square units
where,
 l = Length,
 b = Breadth,
 h = Height,
 S = Total surface area, and
 L = Lateral surface area
For more information, check this interesting article on surface area of cuboid.
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 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
Check out the volume of cuboid section for more.
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Cuboid Examples

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) square units.
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)} square units
= 2 (48 + 24 + 32) square units
= 2 (104) = 208 square unitsTherefore, the surface area of the cuboid 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}) units.
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}) units
= √(25 + 16 + 9) units
= √50
Therefore, the length of the diagonal is √50 units.
FAQs on Cuboid
What is a Cuboid?
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.
How Many Edges a Cuboid has?
A cuboid has 12 edges, 6 faces, and 8 vertices.
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, the width of 4 units, and 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.
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 are the Properties of a Cuboid?
A cuboid is a threedimensional shape that has a length, a width, and a height. The following properties help us identify a cuboid easily:
 A cuboid has 6 faces, 8 vertices, and 12 edges.
 All the angles are right angles.
 All the faces are rectangular in shape.
 Two diagonals can be drawn on each face of a cuboid.
 The opposite edges are parallel to each other.
What is the Difference Between Cube and Cuboid?
Cube and cuboid both 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.
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