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# Volume of Cuboid – Formula, Definition, Examples

## Volume of Cuboid

The number of materials that a cuboid can transport or hold is known as the volume of the cuboid, and it determines the holding capacity of a cylinder. We can determine volume of a cuboid by the formula V= l × b × h  . In this article, we will learn about cuboids, their properties, and the Volume of a cuboid with some solved examples. With we also know about the properties, surface area, and diagonals of a cuboid.

## Volume of Cuboid: Definition of Cuboid

In geometry, A cuboid is a three-dimensional figure or object that has six rectangular faces, each of which has eight vertices and twelve edges.
Now imagine a shape made by stacking numerous congruent rectangles on top of one another. The resultant formed shape is known as a cuboid. In daily life, we observed different cuboid-shaped objects such as The lunch box, Bricks, Shoebox, Book, Carton boxes, and so on. As a cuboid is a three-dimensional solid object, Thus it has length, Height, and width. Let’s understand those quantities of a cuboid in the following diagram.

## Volume of Cuboid: Properties of a cuboid

The properties of a cuboid must be understood before learning about various cuboid quantities. such that we can quickly recognize a cuboid by its characteristics.
The main properties of a cuboid are listed below –
• There are 6 faces, 8 vertices, and 12 edges on a cuboid.
• The edges on either side of each other are parallel
• As a cuboid is a three-dimensional object, it has length, breadth, and height.
• A cuboid has only right angles that are produced at its vertices.
• The shapes of all the faces are rectangles.
• A cuboid has two diagonal lines that can be drawn on each face.

## What is the Volume of a cuboid?

Earlier we know that volume of a cuboid refers to the holding capacity of a cuboid. Basically, the volume of a cuboid refers to the amount that can hold by the cuboid.
The Volume of a cuboid can easily determine by the formula = Length × breadth × height
If we considered a cuboid having l length,h height, and b  breadth. And Volume -V, then

Volume of the cuboid (V) = l × b × h cubic units.

Units used to measure the volume of cuboid is –
Cubic Centimeters (cm³), Cubic meters (m³)

## Surface area of a cuboid

As a Cuboid is a three-dimensional figure, it has two types of surface area –
• Lateral surface area or LSA
• Total surface area or TSA

### Lateral surface area

The total area of all faces, excluding the top and bottom faces of a cuboid, is considered as Lateral surface area.
Lateral surface area = Sum of all 4 faces except the top and the top face of the cuboid.

If we took into account a cuboid with l length, h height, and b width. follows.

Lateral surface area (LSA) = 2h(l + b) sq.units

### Total Surface Area

A cuboid’s surface area is the overall area that it takes up in its shape.
Total surface area (TSA ) equals the sum of the surfaces of all six  rectangular faces

If we considered a cuboid having l length,h height, and b  breadth.  then,

Total surface area (TSA ) =2(lb + bh + hl) sq.units

## Perimeter of  cuboid

We know that a cuboid has 8 faces and 12 edges Perimeter is nothing but the sum of the lengths of all the 12 edges.
Taking into account a cuboid with dimensions of l length, h height, and b width. After that,
Perimeter of Cuboid = 4l + 4b + 4h

= 4× (l + b + h)

Perimeter of Cuboid (P) = 4× (l + b + h) units

## Diagonals of Cuboid

A line segment that joins two of its opposed vertices and traverses the cuboid’s body, is known as a Diagonal cuboid Since a cuboid is a 3D shape, there are two types of diagonals in it:
• Face Diagonals
• Space Diagonals

### Face Diagonals

Face Diagonals are considered as the line segment which is formed by connecting the opposite vertices of a certain cuboid face. Only two diagonals can be formed on each cuboid’s face.
A cuboid has a total of 12 face diagonals since it has 6 faces.

### Space diagonal

A line segment that connects a cuboid’s opposing vertices is known as a space diagonal. The face diagonals have traversed the interior of the cuboid  Thus it is possible to draw 4 space diagonals inside of one cuboid.

The Formulas to determine Diagonals of Cuboid
Face Diagonals of cuboid = √(l² + b²) units
Space Diagonals of Cuboid = √(l²+ b²+ h²) units

Whereas a cuboid’s three primary dimensions are its length (l), its width (b), and its height (h),

## Volume of Cuboid Formula and Other Related Formula

Here is a list consists all cuboid-related formulas in one place. We looked at a cuboid with the dimensions l length, h height, and b width.

 Cuboid’s Quantities Formulas Volume l × b × h cubic units. Total Surface Area (TSA) 2(lb + bh + hl) sq.units Lateral surface area (LSA) 2h(l + b) sq.units Perimeter 4(l + b + h) units Face Diagonals √(l² + b²) units Space Diagonals √(l²+ b²+ h²) units

## How to find the Volume of a Cuboid?- Solved example

Q. What is the volume of a cuboid with the dimensions 16 cm long, 12 cm wide, and 10 cm high?

Solution:

The cuboid’s length is 25 cm.

the cuboid’s width is 12 cm

The cuboid’s height is 16 cm.

As we know, the Volume of the cuboid =  length× breadth ×  height.

V = (25 × 12 × 16) cm³

V = 4800 cm³( Answer)

Q. A cubical measures 8 meters long, 3 meters wide, and 10 meters high. Find the cubical’s volume.

Solution:

Length of the cubical – 8 meters.
cubical’s width – 3 meters
Cubical’s height -10 meters
Since the cubical’s volume is determined by its length, width, and height,
So now, volume = 8×3×10 m³
V = 240 m³ . ( Answer)

Q. Determine the total surface area of a cuboid having a length of 10 cm, a height of 12 cm, and a breadth of 8 cm.

As we know Total surface area (TSA ) = The sum of the surfaces of all six  rectangular faces
If we considered a cuboid having l length,h height, and b  breadth.  then,
Total surface area (TSA ) =2(lb + bh + hl) sq.units
In the given problem,
Length (l)= 10 cm , breadth (b) = 8 cm ,height (h)= 12 cm .

Total surface area = 2[ ( 10×8)+(8×12)+(12×10)]
Or,TSA = 2 × (80+ 96+120)
Or, TSA = 592 cm² (Answer)

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## Volume of cuboid: FAQ

Q. What is the definition of Cuboid in maths?
A cuboid is a three-dimensional figure or object in geometry that has six rectangular faces with eight vertices and twelve edges each.
Examples of cuboids are lunch boxes, Bricks, Shoebox, Book, Carton boxes

Q. How to determine the volume of a cuboid?
the volume of a cuboid refers to the holding capacity of a cuboid.
Basically, the volume of the cuboid refers to the amount that can hold by the cuboid.
The Volume of a cuboid can easily determine by the formula = Length × breadth × height
If we considered a cuboid having l length,h height, and b  breadth. And Volume -V, then

Volume of the cuboid (V) = l × b × h cubic units.

Q. What is the formula for calculating the total surface area of a cuboid?

A cuboid’s surface area is the overall area that it takes up in its shape. It can be calculated by following the formula,
Total surface area (TSA ) = The sum of the surfaces of all six  rectangular faces

If we considered a cuboid having l length,h height, and b  breadth.  then,

Total surface area (TSA ) =2(lb + bh + hl) sq.units

Q. Find out the length of space diagonals of a cuboid having a length of l, breadth b, and height h.
A line segment that connects a cuboid’s opposing vertices is known as a space diagonal. The face diaggonals have traversed the interior of the cuboid  Thus it is possible to draw 4 space diagonals inside of one cuboid.
The Formulas to determine Diagonals of Cuboid
Face Diagonals of cuboid = √(l² + b²) units

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