What is a Volume?

Volume is a measure of the amount of space an object occupies in three-dimensional (3D) space. It represents how much "stuff" can fit inside a 3D object or container, and it's a fundamental concept in geometry, physics, and many real-world applications.

To put it simply, volume is the 3D equivalent of area in two dimensions. While area measures the size of a surface (like a piece of paper or a floor), volume measures the space inside an object (like the amount of water a box can hold).

How is Volume Measured?

Volume is measured in cubic units, which represent a cube where each side is 1 unit long. For example, cubic meters (m³) or cubic centimeters (cm³) are common units of volume.

Examples of Volume in Real Life

1. Box or Cube: A common example of volume is a box (or cube). If you have a box that is 2 meters long, 3 meters wide, and 4 meters tall, the volume of the box is calculated by multiplying its dimensions:
1. Length measures how long something is along the ground (like the football field from one goal to the other).
2. Width measures how wide something is across the ground (from one sideline to the other).
3. Height measures how tall something is, going upward from the ground (like how tall a building is).

What is Length Width Height?

Length, width, and height are used to find the side or dimensions of an object. A figure’s longest side is length, width is the shorter side of a figure and the vertical dimension of the figure is called height.

• Length and width are used in two-dimensional shapes (2D shapes),
• Whereas in three-dimensional shapes (3D shapes), we use the height along with the length and width.

Length

Tool that requires measuring distance between two points, is known as Length. Length is used to measure the longest dimension of a figure. Length is a linear measurement, which is used to measure only the distance separating two points. The units of length are meters, kilometers, centimeters, inches, and so on. As an example of length, we can say, the length of the pitch of a cricket ground is 20 metre long.

Width

Tool that is used to measure the shorter distance of an object or a figure, is called Width. It is the shorter dimension of a figure. Width is a linear measurement which is used to measure only the shorter distance of an object. The units of width are meters, kilometres , centimeters, inches, and so on.

As an example of width, we can say, width of the pitch of a cricket ground is 5 metre long.

Height

Another term of height is Depth. Height or depth is the third vertical dimension of object in 3D shape. It identifies how deep or how high an object is. Units of height are meters, kilometres, centimeters, inches, and so on.

How to Write Dimensions of Length Width Height

Dimensions of length, width, and height can write very easily as we already read the defination of these tools. In a 2D geometrical shape, we get only two dimensions, a length and a width (breadth). In a 3D shape, we get all three dimensions of length, width, and height. The longest side of the figure is labelled as the length. The vertical dimension is written as the height or depth. The remaining side is called width or breadth.

This concept is shown in the above diagram. Units of these dimensions are expressed in units like meters, centimeters, inches, and so on.

Length × Width × Height

When all the three dimensions multiplied together, then we get volume of a geometrical shape. Volume is defined as the quantity of space occupied by a geometrical shape. The volume of a cuboid is equal to the multiplication of its length, breadth, and height. In other words, if we multiply all three dimensions together, we get the volume of a cuboid or any rectangular box.

Mathematically, Volume of a Rectangular Prism (cuboid) or a Box = Length × Width × Height.

For example, if length, width, and height of a rectangular prism is  5, 8 and 10 units respectively, then its volume (V) is, 
V =  5 × 8 × 10. 
V = 400 cube units

Length Vs Width

Length and width both are used to measure distance or dimension of a side but there is a remarkable difference between these two. Length is the longest dimension whereas width is the shortest dimension. Length is always larger than the width. In other words, length denotes a figure’s longer side, while width denotes its shorter side. Width (breadth) gives the wide nature of a geometrical shape while the length tells how long a shape is.

If two measurements of a geometrical shape are given which is 100 cm and 70 cm respectively, then we can easily say that 100 cm is the length and 70 cm is the width.

Length, Width, and Height in Rectangle

A rectangle is an example of 2D shape, so, it has only length and width but a rectangular box or a rectangular prism (cuboid) is 3D shape so that it has all three dimensions: length, width, and height. So, we can say that extensions of rectangular shape in 3D contains length, width, and height.

Rectangular Prism Formulas

There are two formular group for rectangular prisms;

• Volume of Rectangular Prism
•  Surface area of a rectangular prism, which comprise of either Total or Lateral

Volume of Rectangular Prism

Length, Width, and Height are used to calculate volume and surface area of a rectangular prism by using certain formulas. These formulas are given below,

Volume of Rectangular Prism = length × width × height

Surface Areas of a Rectangular Prism: Total vs Lateral

A rectangular prism (or box) has two types of surface areas: Total Surface Area (TSA) and Lateral Surface Area (LSA). Let’s break down what each of these means:

1. Total Surface Area (TSA)

The total surface area is the sum of the areas of all six faces of the rectangular prism. This includes both the side faces and the top and bottom faces (called the bases).

You can calculate the total surface area with this formula:

TSA = 2(length × width + width × height + height × length)

Total Surface Area of Rectangular Prism = 2 [(length × width) + (width × height) + (length × height)]

This formula works because the rectangular prism has:

• Two length × width faces (top and bottom),
• Two width × height faces (side faces),
• Two height × length faces (front and back).

2. Lateral Surface Area (LSA)

The lateral surface area is the sum of the areas of only the side faces, meaning it excludes the top and bottom (the bases). You’re only looking at the four vertical faces of the prism.

The formula for lateral surface area is:

LSA = 2(width × height + height × length)

Lateral Surface Area of Rectangular Prism = 2 [(length × width) + (width × height)]