 # Volume Of Cuboid

Volume of cuboid is the total space occupied by the cuboid in a three-dimensional space. A cuboid is a three-dimensional structure having six rectangular faces. These six faces of the cuboid exist as a pair of three parallel faces. Therefore, the volume is a measure based on the dimensions of these faces, i.e. length, width and height. Surface area of cuboid is the total area covered by its faces.

 Volume of Cuboid = Length x Width x Height  (Cubic Unit)

When the area of the faces of a cuboid is same, we call this cuboid as a cube. The area of all the faces of a cube is the same as they are all squares. Read about 3d shapes here.

Think of a scenario where we need to calculate the amount of sugar that can be accommodated in a cuboidal box. In other words, we mean to calculate the capacity of this box. The capacity of a cuboidal box is basically equal to the volume of cuboid involved. In this article, let us discuss what is a volume of a cuboid, its formula, along with the volume of a cuboid prism and a cube example.

## What is the Volume of a Cuboid?

The volume of a three-dimensional shape Cuboid, in general, is equal to the amount of space occupied by the shape cuboid. The term “Solid Rectangle” is also known as a cuboid, because all the faces of a cuboid are rectangular.  In rectangular cuboid, all the angles are at right angles and the opposite faces of a cuboid are equal.

The general formula for the calculation of the volume of a cuboid is given below.

The volume of cuboid: The volume of a cuboid is given by the product of its dimensions.

The volume of a cuboid of length ‘l’, breadth ‘b’, height ‘h’ = l×b×h cubic units

Also, try: Volume of Cuboid Calculator

## Total Surface Area of Cuboid

The total surface area of a cuboid is equal to the sum of the areas of the six rectangular faces whereas the Lateral surface area of a cuboid equal to the sum of the four rectangular faces, in which two rectangular faces of the top and bottom faces are excluded. The formula for the total surface area and lateral surface area of a cuboid is given as:

Total Surface Area of a Cuboid = 2 (lb + hb + lh) square units

Lateral Surface Area of a Cuboid = 2h (l+b)

Now, let us discuss the volume of a cuboid in detail.

## Volume of a Cuboid Prism

A cuboid prism or a rectangular prism is the same as the cuboid. It has 6 faces, 8 vertices, and 12 edges. When a cuboid prism or a rectangular prism has a rectangular cross-section. A prism is called right prism when the angle between the base and the sides are at right angles. Also, the top and the bottom surfaces are in the same shape and size.  The volume of the cuboid prism is given as:

Volume of a cuboid prism or rectangular prism, V= length × breadth × height (cubic units)

## Volume of a Cube

Volume of cube: Cuboid in which length of each edge is equal is known as a cube. Thus,

Volume of a cube of side ‘a’ = a3

### Video Lesson ## Solved Examples

Question 1: Calculate the length of the edge of a cube-shaped container of volume 216 m3.

Solution: Volume of a cube= a3

=> a3= 216

=> a = 6 m

Question 2: Calculate the amount of air that can be accumulated in a room that has a length of 5 m, breadth of 6 m and a height of 10 m.

Solution: Amount of air that can be accumulated in a room = capacity of the room = volume of a cuboid

Volume of cuboid = l×b×h = 5 ×6 ×10 = 300 m3

Thus, this room can accommodate the maximum of 300 m3 of air.

## Practice Questions

Find the volume of cuboid with following dimensions:

• Length = 15 cm, Breadth = 50 cm and Height = 22 cm
• Length = 7 m, Breadth = 3 m and Height = 5 m
• Length = 2 m, Breadth = 2.5 m and Height = 1.5 m
• Length = 80 cm, Breadth = 20 cm and Height = 44 cm
• Length = 1.7 m, Breadth = 1.5 m and Height = 1 m

To learn and practice more problems in the surface area of cuboid, you can visit BYJU’S – The Learning App

## Frequently Asked Questions – FAQs

### What is the formula for volume of cube and cuboid?

Volume of cuboid is the product of length, width and height.
V (cuboid) = Length x Width x Height (cubic units)
Volume of cube is equal to the cube of its side (all the sides are equal in length).
V (cube) = Side3

### How do we define volume of cuboid?

Volume of cuboid is defined as the amount of space occupied by the walls of cuboid in a three-dimensional space.

### Does the order of cuboid matters to calculate the volume?

It does not matter, if a cuboid is kept vertically or horizontally. The volume of the cuboid remains same even if we change the order of its length, width and height.

### Find the volume of cuboid if length = 14cm, width = 50cm and height = 10cm.

Given, length = 14cm, width = 50cm and height = 10cm.
Volume of cuboid = length x width x height
V = 14 x 50 x 10
V = 7000 cu.cm.

### If the units of dimensions of cuboid are different, then how to find the volume?

If the units of length, width and height are different then, we need to convert them into same unit first and then find the volume.
For example, length = 10cm, width = 10mm, height = 10 cm
Since, width is in millimeters, therefore, we will convert first into cm
1cm = 10 mm
So, width = 1cm
Therefore, volume = 10 x 1 x 10 = 100 cu.cm