Cuboid

 

A cuboid is a 3D solid figure with six rectangular faces, twelve edges, and eight vertices. Also known as a rectangular prism, the cuboid shape is commonly found in everyday objects like books, boxes, and bricks. In geometry, understanding the cuboid formula, dimensions, and properties is essential for solving surface area and volume problems.

This guide covers everything about the cuboid, from its definition and components to solved examples and real-life relevance.

 

Table of Contents

• What is a Cuboid?
• Cuboid Shape
• Faces, Edges and Vertices of Cuboid
• Properties of Cuboid
• Surface Area of Cuboid
• Lateral Surface Area of Cuboid
• Total Surface Area of Cuboid
• Volume of Cuboid
• Diagonal of Cuboid
• Perimeter of Cuboid
• Cuboid Formula
• Cuboid Net
• Solved Examples on Cuboid
• Practice Questions
• Conclusion
• FAQs on Cuboid

 

What is a Cuboid?

A cuboid is a solid geometric figure with three dimensions: length, width, and height. It has six rectangular faces, with each pair of opposite faces being equal and parallel. The cuboid has:

• 6 faces

• 8 vertices

• 12 edges
  
  

According to Euler's formula for 3D shapes:
Faces + Vertices = Edges + 2
So, for a cuboid: 6 + 8 = 12 + 2 

 

Cuboid Shape

The cuboid shape is defined by its rectangular faces. Each face meets another at a 90° angle, making the cuboid a right-angled prism. When all edges are of equal length, the cuboid becomes a cube. This makes understanding the cuboid the foundation for learning other 3D shapes.

 

Faces, Edges and Vertices of Cuboid

• Faces: 6 rectangular faces

• Edges: 12 straight edges

• Vertices: 8 corner points
  
  

Example face pairs:

• Top & bottom: ABCD and EFGH

• Side faces: ABFE, DCGH, etc.
  
  

This structure helps visualize how the cuboid shape is formed.

 

Properties of Cuboid

Some important properties of cuboid include:

• All faces are rectangles

• Opposite edges are equal and parallel

• Each corner forms a 90° angle

• Three dimensions: length (l), breadth (b), height (h)

• Can have square faces but not necessarily
  
  

These cuboid properties are consistent across all rectangular prisms.

 

Surface Area of Cuboid

The surface area of a cuboid is the sum of areas of all six faces.

Formula:

TSA = 2(lb + bh + hl)

Where:

• l = length

• b = breadth

• h = height
  
  

Surface area of cuboid helps in calculating material needed to wrap or cover a 3D object.

 

Lateral Surface Area of Cuboid

The lateral surface area (LSA) includes the area of all sides except the top and bottom.

Formula:

LSA = 2h(l + b)

This is used in real-life problems involving walls or side coverings.

 

Total Surface Area of Cuboid

The total surface area of cuboid adds all six face areas.

Formula:

TSA = 2(lb + bh + hl)

Example:
If l = 5 cm, b = 3 cm, h = 2 cm
Then TSA = 2(5×3 + 3×2 + 2×5) = 2(15 + 6 + 10) = 2×31 = 62 cm²

 

Volume of Cuboid

The volume of a cuboid is the space it occupies in 3D.

Formula:

Volume = l × b × h

This helps measure capacity or storage in real-world cuboids like tanks, boxes, etc.

 

Diagonal of Cuboid

The diagonal of a cuboid is the longest straight line between opposite corners.

Formula:

Diagonal = √(l² + b² + h²)

This space diagonal connects two farthest points inside the cuboid.

 

Perimeter of Cuboid

The perimeter of cuboid adds up all the edge lengths.

Formula:

Perimeter = 4(l + b + h)

It helps calculate total external edges in construction or framing.

 

Cuboid Formula

These are the most used cuboid formulas in math and science.

 

Cuboid Net

A cuboid net is the 2D layout obtained by unfolding the cuboid. It helps visualize all six faces.

There are 54 different nets possible for a cuboid with unequal sides. These are useful in packaging design and folding activities.

 

Solved Examples on Cuboid

Example 1:
Find the volume of cuboid with l = 10 cm, b = 8 cm, h = 4 cm
Volume = l × b × h = 10 × 8 × 4 = 320 cm³

Example 2:
Find the LSA and TSA of a cuboid with l = 12 cm, b = 7 cm, h = 5 cm
LSA = 2h(l + b) = 2×5(12 + 7) = 10×19 = 190 cm²
TSA = 2(lb + bh + hl) = 2(84 + 35 + 60) = 358 cm²

 

Practice Questions

1. Find the surface area and volume of a cuboid with dimensions 3 cm × 2 cm × 1.5 cm

2. Calculate the perimeter of a cuboid with l = 6 cm, b = 4 cm, h = 3 cm

3. What is the diagonal of a cuboid with l = 7.5 cm, b = 3.5 cm, h = 5 cm?

4. List all faces, edges, and vertices of a cuboid

5. Find TSA and LSA of a cuboid-shaped gift box measuring 10 cm × 6 cm × 4 cm
   
   

 

Conclusion

The cuboid is a crucial concept in 3D geometry, used widely in packaging, architecture, and everyday math. Understanding cuboid formulas like surface area, volume, and diagonal enables students to solve real-world problems effectively. Whether it’s calculating the size of a storage box or visualizing shapes in engineering, the cuboid plays a major role.

 

Related Links :  

Volume of Cube and Cuboid : Master the formulas for volume of cube and cuboid with real-life examples and practice questions. Learn easily at Orchids The International School!

Frequently Asked Questions on Cuboid

1.What is a cuboid?

Ans. A cuboid is a three-dimensional shape with 6 rectangular faces, 8 vertices, and 12 edges.

2. What is the difference between cube and cuboid?

Ans. A cube has all equal square faces; a cuboid has rectangular faces with different dimensions.

3. What are the cuboid formulas?

Ans. Key formulas include:

• Volume = l × b × h

• TSA = 2(lb + bh + hl)

• Diagonal = √(l² + b² + h²)

• Perimeter = 4(l + b + h)
  
  

4. Is cuboid the same as rectangular prism?

Ans. Yes, a cuboid is also called a rectangular prism.

5. Can a cuboid have square faces?

 Ans.Yes, if two adjacent sides are equal, that face becomes a square.

 

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