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Volume of Cuboid | Formula and Examples

Last Updated : 18 Apr, 2024
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Volume of a cuboid is calculated using the formula V = L × B × H, where V represents the volume in cubic units, L stands for length, B for breadth, and H for height. Here, the breadth and width of a cuboid are the same things. The volume signifies the amount of space occupied by the cuboid in three dimensions. To measure it, multiply the length by the breadth and then by the height of the cuboid. Each dimension contributes to the overall capacity of the cuboid, with the product yielding the total volume encompassed by its shape.

Volume of a Cuboid = length × breadth × height

A cuboid is a convex polyhedron surrounded by 6 rectangular faces with 8 vertices and 12 edges. Volume of the Cuboid is the space occupied by the cuboid in the 3D space.

Volume of Cuboid Diagram

Let’s learn the formula for the Volume of Cuboid and how to use it with the help of solved examples.

What is Volume of Cuboid?

Volume of a Cuboid is total space occupied by surfaces of cuboid.

We can also say that volume of cuboid is total volume of material that is used to make solid cuboid.

Volume of Cuboid Formula

A cuboid is a three-dimensional structure with six rectangular faces. The volume of cuboid formula is based on the dimensions of these faces: length, width, and height.

Volume of a Cuboid Formula:

Volume of Cuboid = Length × Breadth × Height (cubic units)

Volume of Cuboid Derivation

Let’s assume the length, breadth and height of the cuboid to be ‘l’ , ‘b’, and ‘h’ units respectively.

Derivation of Volume of Cuboid Formula

Deriving the Formula for Volume of Cuboid

Now, we divide the cuboid into smaller cubes along its length, width, and height.

There will be ‘l’ unit cubes along the length, ‘b’ unit cubes, ‘h’ unit cubes along the height.

Total number of unit cubes = l × b × h

Volume of each of these unit cubes = 1 cubic unit.

Total volume of the cuboid (V) = Total number of unit cubes = l × b × h

Therefore, the formula for the volume of a cuboid is:

V = l × b × h = lbh

How to Find Volume of Cuboid?

Steps needed to calculate the volume of a cuboid are as follows:

Step 1: Check that the dimensions of the given cuboid are in the same units. If not, convert the dimensions to the same units.

Step 2: Multiply length, width, and height of cuboid when dimensions are in same units.

Step 3: Result is Volume of Cuboid.

Volume of Cuboid in Litres

To calculate volume of a cuboid in liters, we need to follow these steps:

Step 1: First, we measure the Length, Width, and Height of the cuboid in centimeters (cm).

Step 2: Then the volume is calculated in cubic centimeters (cm³) using the formula:

Volume = Length (cm) × Breadth (cm) × Height (cm)

Step 3: The volume is converted from cubic centimeters (cm³) to liters (L). There are 1000 cubic centimeters in 1 liter, so you can use the following conversion factor:

1 liter = 1000 cm³

Step 4: The calculated volume in cubic centimeters is divided by 1000 to get the volume in liters:

Volume (L) = Volume (cm³) / 1000

Example:

Let us take a cuboid with the following dimensions:

Length = 20 cm, Width = 10 cm, Height = 5 cm

  • Volume in cubic centimeters:

Volume = 20 cm x 10 cm x 5 cm = 1000 cm³

  • Volume in liters:

Volume (L) = 1000 cm³ / 1000 = 1 liter

Volume of Cube and Cuboid

A cube is a special type of cuboid in which the length, breadth, and height is equal.

Volume of Cube Formula:

Volume of a Cube of Side ‘a’ = a3 unit3

Surface Area of Cuboid

Surface area of a cuboid is combined area of all its six rectangular faces. To find it, simply add up the areas of all these faces.

We can find surface area of a cuboid using formula:

Total Surface Area (TSA) = 2lw + 2lh + 2hw = 2(lw + lh + hw)

Here, l represents the length, w is the width, and h stands for the height.

Additionally, lateral surface area of a cuboid can be determined by formula:

Lateral Surface Area (LSA) = 2(lh + wh) = 2h(l + w)

Volume of a Cuboid Prism

A rectangular prism or cuboid prism and a cuboid are two terms often used interchangeably to describe the same three-dimensional geometric shape. Both refer to a solid figure with six rectangular faces, where each face is perpendicular to its adjacent faces.

Cuboid

Rectangular Prism / Cuboid Prism

This term is often used in geometry and engineering to specifically describe a rectangular prism where the lengths of its edges are all different. In other words, a cuboid has rectangular faces, but its dimensions (length, width, and height) are not necessarily equal.

This term is more commonly used in mathematics and geometry to describe a three-dimensional figure with six faces that are all rectangles. It’s a general term that encompasses any prism with rectangular faces, including cubes.

Hence, the volume of a cuboid prism or volume of a rectangular prism are same as volume of a cuboid which is given by:

Volume = length × width × height

where:

  • length is the longest side of the base
  • width is the shorter side of the base
  • height is the distance from the base to the opposite side

Related Articles:

Volume of Cube

Volume of Cone

Volume of Sphere

Volume of Cylinder

Solved Questions on Volume of Cuboid

Let’s solve some sample problems on the volume of cuboid.

Question 1: A cuboid has dimensions of 6 cm, 8 cm, and 10 cm. What is its volume?

Solution:

Given: 

  • l = 6 cm
  • w = 8 cm
  • h = 10 cm

Volume = Length × Width × Height

⇒V = (6)(8)(10) = 480 cm3

Therefore, volume of cuboid is 480 cubic centimeters.

Question 2: If you cut the length of one side by half, how will the volume of cuboid change?

Solution: 

Original Volume  = l × b × h 

If new length = l/2

⇒ New Volume = (l/2) × b × h 

⇒ New Volume = (lbh)/2 

⇒ New Volume = Original Volume/2. 

Thus, volume of a cuboid is halved as soon as its length is halved.

Question 3: If a cube has a volume of 3000 cm3, a width of 10 cm, and a height of 10 cm, what is the length?

Solution:

Volume of a Cuboid = length × width × height

Given:

  • Volume of Cuboid = 3000 cm3
  • Width of Cuboid = 10 cm
  • Height of Cuboid = 10 cm

Let, length of the Cuboid be x cm

Thus, 

Volume = 3000 cm3

⇒  x × 10 × 10 = 3000

⇒ x = 3000/100

⇒ x = 30 cm

Thus, length of a cuboid is 30 cm.

Volume of Cuboid Practice Questions

Here are a few Practice Questions on Volume of Cuboid for you to solve.

Q1: Find Volume of a Cuboidal Tank of length 1m, width 0.5m and height 2m.

Q2: Find length of a Cuboid whose volume is 300 cubic metres and breadth and height are 20 m and 30 m respectively

Q3: Find number of bricks each of dimension 0.2m ⨯ 0.05 m ⨯ 0.1 m to construct a wall of 2 m ⨯ 4 m ⨯ 0.5 m

Q4: Find amount of water flowing out of a canal in 1 hour whose breadth is 10 m, depth is 4 m and water flowing rate is 1 m/s.

FAQs on Volume of Cuboid

What is a Cuboid?

A cuboid is a 3-Dimensional shape which is bounded by the six rectangular faces.

What is the Volume of Cuboid?

Formula for volume of a cuboid is given by:

Volume = Length × Width × Height

What are Units for Volume of Cuboid?

As volume is product of three lengths, unit of volume is cubic units, such as cm3, m3, Km3, etc.

Can Volume of Cuboid be Negative?

As volume of cuboid represent the space occupied by the cuboid in the three dimensional space, it can’t be negative. It can only be positive or zero.

How to Find the Length of Cuboid? 

Volume of a cuboid is equal to length × width × height. 

Given volume, width, and height, 

We can write 

v = l×b×h

l = v/bh

What is Surface Area of Cuboid?

Surface Area of a Cuboid can be found using the following formula:

Surface Area = 2lw + 2lh + 2wh

What is volume of a cuboid with example?

Volume of a cuboid is the measure of space it occupies in three dimensions. It can be calculated using the formula: Volume = length × breadth × height.

For example, if a cuboid has a length of 5 units, a breadth of 3 units, and a height of 2 units, its volume would be 5 × 3 × 2 = 30 cubic units.

What is breadth of a cuboid?

Breadth of a cuboid is one of its dimensions, representing the measure of its side that is perpendicular to its length and height.

What is SI unit for volume?

SI (International System of Units) unit for volume is the cubic meter (m³). This unit is used to measure the amount of three-dimensional space that an object occupies. However, for smaller objects, cubic centimeters (cm³) or cubic millimeters (mm³) are also commonly used.



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