# Volume of Cuboid

Volume of Cuboid is the space occupied by the cuboid or cuboid-shaped object in the 3D space. In 3D-Geometry, a cuboid is the first fundament form which is represented by the three lengths. It is a convex polyhedron surrounded by 6 rectangular faces with 8 vertices and 12 edges.

In real life, we can observe that there are a lot of objects around us that have cuboidal forms. In this article about the “Volume of Cuboid,” we will learn about the cuboid and how to calculate the volume of Cuboid.

Surface Area of Cuboid is also a very important Formula along with volume of cuboid and it is the total area covered by its rectangular faces.

## Cuboid Definition

A cuboid in 3D solid which can be represendted by three lengths: length, width, and height. It is made up of 6 rectangular faces with 8 vertices and 12 edges.  A perfect cuboid is a cuboid with integer edges.

We know that a rectangle is a two-dimensional figure with four sides. Now imagine the shape formed when many congruent rectangles are placed on top of other rectangles. This shape is called a cuboid. Notice the following cuboid showing three dimensions: length, width, and height.

### Cuboid Shape

The shape of a cuboid is a closed 3D shape surrounded by a rectangular surface, that is, a flat area of rectangle. The shape of the cuboid is shown in the figure below.

## What is Volume of Cuboid?

The volume of a Cuboid is the total space occupied by the surfaces of the cuboid. We can also say that the volume of the cuboid is the total volume of the material that is used to make the solid cuboid. It is measured in unit cubes, i.e. m3, cm3, etc. The volume of the cuboid is calculated by the formula discussed below,

### Volume of Cuboid Definition:

Volume of Cuboid is a measure of the three-dimensional space that the cuboid occupies.

## Volume of Cuboid Formula

Volume of cuboid is the total space that the box occupies in three-dimensional space. A cuboid is a three-dimensional structure with six rectangular faces. These six faces of a cuboid exist as a pair of three parallel faces. Therefore, volume is a measure based on the dimensions of these faces: length, width, and height. It is measured in cubic units.

Volume of cuboid = Length Ã— Width Ã— Height (cubic unit)

## How to find Volume of Cuboid?

As we know the volume of a cuboid is the space it occupies inside the cuboid and it can be calculated using the cuboid volume formula. One must know about how to find volume of the cuboid. The 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 the length, width, and height of the cuboid when the dimensions are in same units.

Step 3: The result is the Volume of Cuboid.

Example: Calculated the volume of the cuboid with length 1 m, width  0.75 m, and height 200 cm.

Solution:

As, 1 m = 100 cm,

Length = 1 m = 100 cm

Width = 0.75 m = 75 cm

Height = 200 cm

Thus, Volume of Cuboid = 100  Ã— 75 Ã— 200

⇒ Volume of Cuboid = 15,00,000 cm3

As, 10,00,000 cm3 = 1m3

⇒ Volume of Cuboid = 1.5 m3

## Surface Area of Cuboid

The surface area of a cuboid is defined as the area of the surface of the faces of the cuboid. In a cuboid, we have 6 faces, for a cuboid we can have two types of surface area, Curved Surface Area and Total Surface Area. Now let’s learn the formula for the same.

• Total Surface Area of a Cuboid = 2 (lb + hb + lh) square units
• Lateral Surface Area of a Cuboid = 2h (l+b)

## Volume of Cube

A cube is a special type of cuboid in which the length, breadth, and height is equal. The volume of Cube is calculated as,

Volume of a cube of side ‘a’ = a3 unit3

Related Resources,

## Sample Problems on Volume of Cuboid

Problem 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 Ã— Width Ã— Height

⇒V = (6)(8)(10) = 480 cm3

Therefore, the volume of the cuboid is 480 cubic centimeters.

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

Solution:

Original Volume  = l Ã— b Ã— h

If new length = l/2

⇒ New Volume = (l/2) Ã— b Ã— h

⇒ New Volume = (lbh)/2

⇒ New Volume = Original Volume/2.

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

Problem 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 is = length Ã— width Ã— height

Given:

• Volume of Cuboid =3000 cm3
• Width of Cuboid =10 cm
• Height of Cuboid =5 cm

Let, the length of the Cuboid be x cm.

Thus,

Volume = 3000 cm3

⇒  xÃ—10Ã—5 = 3000

⇒ x = 3000/50

⇒ x = 60 cm

Thus, length of a cuboid is 60 cm.

Problem 4: Cuboidal fish tanks have dimensions of 30 inches, 20 inches, and 15 inches. Can you determine the volume of an aquarium with fish?

Solution:

Given:

• Length of the aquarium = 30 inches
• Width of the aquarium = 20 inches
• Height of the aquarium = 15 inches

As, Volume = Length Ã— Width Ã— Height

⇒ Volume = 30 Ã— 20 Ã— 15 inches3 = 9000 inches3

Thus, the tank has a volume of 9000 cubic inches.

Example 5: A cuboid has a volume of 5000 cubic meters and a width of 25 meters. If its length is twice its height, what are the dimensions of the cuboid?

Solution:

Given:

WIdth = 25 m

Let us consider Length and Height be l m and h m respectivly.

ATQ: Length is twice its height i.e., l = 2h

As, Volume = Length Ã— Width Ã— Height

⇒ 5000 = (2h)(25)(h)

⇒ 5000 = 50h2

⇒ h2 = 100:

⇒ h = 10 m

Thus, l = 2h = 20 m

Therefore, the dimensions of the cuboid are 20 meters by 10 meters by 25 meters.

## Practice Questions on Volume of Cuboid

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

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

Q3: Find the 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 the 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

### 1. What is a Cuboid?

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

### 2. What is Formula for Volume of a Cuboid?

Formula for the volume of a cuboid is given by:

Volume = Length Ã— Width Ã— Height

### 3. What are the Units for the Volume of a Cuboid?

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

### 4. Can the Volume of a 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.

### 5. How to Find the Length of a Cuboid?

The volume of a cuboid is equal to length Ã— width Ã— height.

Given the volume, width, and height,

We can write

v = lÃ—bÃ—h

l=v/bh

### 6. Does Order of Cuboid Matter for Volume Calculations?

It doesn’t matter whether you hold the cuboid vertically or horizontally. The volume of a cuboid is the same even if you change the order of length, width, and height.

### 7. How to Find the Volume of Cuboid?

The volume of a cuboid is calculated by multiplying its length, width, and height.
V = l Ã— b Ã— h

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