Table of Contents

## 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