Volume of Cuboid

Introduction to Volume of Cuboid

The volume of cuboid is the measure of how much space a three-dimensional box-shaped object can hold. A cuboid has three dimensions: length, width and height. It looks like a rectangular box, and examples of daily life include books, bricks and storage boxes.

The volume of a cuboid tells us the total space inside it. In simple words, it shows how many unit cubes can fit perfectly within cuboids. The formula for calculating the volume is very easy:

Volume = Length × width × height

This formula quickly helps us find the capacity of cuboid-shaped things.

Understanding the volume of a cuboid is useful in both mathematics and real life. This helps us to know how much water a tank can store, how much space there is in a container, or the capacity of a box. In this article we learn the formulas for a cuboid volume, solved examples and real-world applications.

 

Table of Contents  

• What is a Cuboid?
• Volume of Cuboid Formula
• How to Find Volume of Cuboid?
• Total Surface Area of Cuboid
• Volume of a Cuboid Prism
  • Volume of a Cube
• Solved Examples
• Practice Questions
• FAQs on Volume of Cuboid

 

What is a Cuboid?

A cuboid is a three-dimensional solid shape with six rectangular faces. Each face meets the other at right angles, making it a type of rectangular prism. It's a cuboid that has:

• 6 faces

• 12 edges

• 8 vertices

All the internal angles of a cuboid are 90°, and the opposite faces are equal in shape.

Examples of cuboids in daily life:

• A brick

• A shoebox

• A matchbox

 

Definition 

The volume of a cuboid is the total space enclosed by it. This tells us how much three-dimensional space the cuboid occupies and is measured in cubic units such as cm³, m³, or in³.

With simple words:

Volume = Space inside the cuboid

This means that the volume shows how much material or content a cuboid-shaped object can hold.

 

Volume of Cuboid Formula

To calculate the volume of a cuboid, we use the standard formula:

Volume of Cuboid = Length (L) × Breadth (B) × Height (h)

Where:

• Length (L): The longest side of the base.

• Breadth (B): The smaller side of the base.

• Height (H): The vertical side of the cuboid.

so,

Volume = 𝑙 × 𝑏 × ℎ

 

Unit of Volume 

The volume of a cuboid depends on the units of its dimensions:

• If dimensions are in cm, volume is in cm³.

• If dimensions are in m, volume is in m³.

• If dimensions are in inches, volume is in in³.

Conversion table for Volume units

 

How to Find Volume of Cuboid?

The volume of a cuboid is the amount of space occupied by it. To calculate the volume, we use its three dimensions: length, breadth (width), and height.

If all three dimensions are equal, the cuboid becomes a cube, since all faces are squares. However, in most real cases, the length, width, and height are different.

 

Example Scenario:

Imagine you want to calculate how much sugar can be inside a cuboidal box. The total capacity of the box is nothing but the volume. When we know the length, width, and height of the box, we can easily calculate the volume using the formula:

Volume of Cuboid = Length (L) × Breadth (B) × Height (h)

 

Steps to find the volume of a cuboid:

• Note the dimensions of the cuboid: length, width, and height.

• Check the units of all dimensions. If they are different, you can change them to the same device.

• Multiply length × breadth × height.

• Write answers in cubic devices (e.g., cm^3, m^3, in^3).

 

Total Surface Area of Cuboid

• The total surface area (TSA) of a cuboid is the sum of the areas of all 6 rectangular faces.

• The lateral surface area (LSA) of a cuboid is the sum of the areas of the four vertical faces.

Formulas:

Total Surface Area = 2(lb + bh + lh) square units

Lateral Surface Area = 2h (l+b) square units

 

Volume of a Cuboid Prism

A cuboid prism is the same as a cuboid. It has 6 faces, 12 edges, and 8 vertices. When the cross-section of a prism is rectangular, it is called a rectangular prism.

If the angle between the base and the sides is 90°, it is called a right prism. In this case, the surfaces on top and bottom are identical just in shape and size.

Formula:

Volume of a Cuboid Prism = 𝑙 × 𝑏 × ℎ (cubic units)

 

Volume of a Cube

• A cube is a special cuboid where all sides are equal (L = B = H = A).

• It has 6 square faces, 12 similar edges, and 8 vertices.

Formula:

Volume of Cube = a^3 cubic units

 

Solved Examples

Example 1: Small Box
A pencil box is the shape of a cuboid. Its length is 20 cm, its breadth is 8 cm, and its height is 5 cm. Find its volume.

Solution:

Volume = l × b × h 

= 20 × 8 × 5

= 800 cm³

 

Example 2: Water Tank

A cuboid-shaped water has length 5 cm, breadth 4 m, and height 3 cm. Find how much water it can hold.

Solution:

Volume = l × b × h 

= 5 × 4 × 3

= 60 m^3 

 

Example 3: Book Covering

A book is in the shape of a cuboid with a length of 25 cm. Breath 18 cm, and height 4 cm. Find the total surface area.

Solution:

TSA = 2 (lb + bh + lh)

= 2 (25 × 18 + 18 ×  4 + 25 × 4)

= 2(450 + 72 + 100)

= 2 (622)

= 1244 cm^2

 

Practice Questions

1. A cuboid has length 10 cm, breadth 6 cm, and height 4 cm. Find its volume.

2. A cupboard is in the shape of a cuboid. Its length is 2 m, breadth is 1.5 m, and height is 1 m. Find its volume.

3. The dimensions of a cuboid-shaped matchbox are 5 cm, 3 cm, and 2 cm. Find its volume.

4. A cuboid-shaped aquarium has a length of 50 cm, a breadth of 30 cm, and a height of 40 cm. Find the volume of water it can hold.

5. A wooden block is a cuboid of length 15 cm, breadth 10 cm, and height 8 cm. Find its volume.

 

Frequently Asked Questions on Volume of Cuboid

1. What is the formula for the volume of a cuboid?

Answer: The volume of a cuboid is found by multiplying its length, breadth (width), and height.

𝑉 = 𝐿 × 𝐵 × 𝐻

It tells us how much space the cuboid takes inside.

 

2. What is the Total Surface Area (TSA) of a cuboid?

Answer: The TSA of a cuboid is the total area of all its six faces.

𝑇𝑆𝐴 = 2 (𝐿𝐵 + 𝐵𝐻 + 𝐿𝐻)

It shows how much paper or paint is needed to cover the cuboid.

 

3. How many faces, edges, and corners does a cuboid have?

Answer: A cuboid has:

• 6 faces (all rectangular)

• 12 edges

• 8 corners (also called vertices)

 

4. A cuboid has length = 12 cm, breadth = 5 cm, and height = 3 cm. What is its volume?

Answer: 𝑉 = 𝐿 × 𝐵 × 𝐻 = 12 × 5 × 3 = 180 cu. cm.

So, the volume is 180 cubic cm.

 

5. Can two cuboids have the same volume but different surface areas?

Answer: It is possible. If two cuboids have different dimensions but the product of their length × breadth × height is the same, then their volume will be the same. But since the faces are different in size, the surface areas can change.